**4. Conclusions**

The finite element method (FEM) offers an option for the solution of complex problems in engineering with a multiphysical profile and equations difficult to solve analytically. The model presented in this chapter, and developed on the COMSOL

#### **Figure 10.**

*Comparison among (a) Vickers microhardness and (b) amplitude and (c) phase signals of PTR applied to brass samples.*

**71**

256923.

*Analysis of the Absorption Phenomenon through the Use of Finite Element Method*

Multiphysics platform, is a basic approach to the application of the law of Lambert– Beer applied to the phenomenon of the absorption of laser light in a material. Due to the multiphysics profile of the program, it is possible to complement the model with other modules of the platform as geometrical optical to modified characteristics of

In the program it is considered that the definition of the mesh is one of the key points to obtain a good simulation that its erroneous choice the design of the same can cost the execution time of the program, or in the worst of the cases a bad

The phenomenon of light absorption influences materials differently, depending on their physical–chemical properties such as thermal diffusivity, density, conductivity, and heat capacity. In the experimental results shown, it can be seen that the thermal treatments that involve the absorption phenomenon induce changes in the mechanical properties of the materials, such as microhardness. As reported in the Kunial brass samples analyzed, the PHT affected its metallurgical,

A marked correlation was found between the FWHM and the diffusivity. The diffusivity increased as the FWHM-1 increased. The highest diffusivity corresponds

The PTR amplitude signal was more sensitive than the PTR phase signal to observe the effect of the PHT temperature on alpha brass thermal, structural, and

Among the possible improvements to the program are the inclusions of the modulation of the light source, which is a very important factor in the photothermal radiometry technique (PTR). The thermal wave generated in the material is very weak and necessarily requires an amplification. Without the modulation of the light source, the amplitude and phase parameters describing the thermal wave would not be possible to capture due to the amount of interference present in the medium. It is important to mention that the modulation frequency of the incident beam directly influences the penetration length in the material and consequently the propagation

With a more detailed theoretical**–**experimental analysis, it is possible to arrive at a comparable result between both parties, either by making measurements directly from temperature variations in the samples analyzed or by defining the variables and conditions in the program that allow obtaining the parameters of amplitude

The authors thank Mario Enrique Rodríguez-Garcia of the Center of Applied Physics and Advanced Technology (CFATA, UNAM) for the support received for carrying out the experiments, the program Cátedras-CONACYT, and the National Council for Science and Technology (CONACyT) for funding through project

It is clear that the theoretical results obtained in COMSOL describe temperature variations as a function of the penetration depth of the incident radiation in the material, which in turn depends on factors such as the incident power. Because in the photothermal radiometry technique the thermal wave captured by the detector is translated as amplitude and phase signals, it is not possible to correlate both results. However, it is clear that a finite element analysis such as that offered by COMSOL offers the advantage of inferring the behavior of the variables involved in

*DOI: http://dx.doi.org/10.5772/intechopen.86924*

laser beam incident in the material.

thermal, and mechanical properties.

Vickers microhardness properties.

the process.

of the thermal wave.

**Acknowledgements**

and phase of the generated thermal wave.

to 700°C while the lowest to the SHT sample.

convergence, translated into erroneous results.

## *Analysis of the Absorption Phenomenon through the Use of Finite Element Method DOI: http://dx.doi.org/10.5772/intechopen.86924*

Multiphysics platform, is a basic approach to the application of the law of Lambert– Beer applied to the phenomenon of the absorption of laser light in a material. Due to the multiphysics profile of the program, it is possible to complement the model with other modules of the platform as geometrical optical to modified characteristics of laser beam incident in the material.

In the program it is considered that the definition of the mesh is one of the key points to obtain a good simulation that its erroneous choice the design of the same can cost the execution time of the program, or in the worst of the cases a bad convergence, translated into erroneous results.

The phenomenon of light absorption influences materials differently, depending on their physical–chemical properties such as thermal diffusivity, density, conductivity, and heat capacity. In the experimental results shown, it can be seen that the thermal treatments that involve the absorption phenomenon induce changes in the mechanical properties of the materials, such as microhardness. As reported in the Kunial brass samples analyzed, the PHT affected its metallurgical, thermal, and mechanical properties.

A marked correlation was found between the FWHM and the diffusivity. The diffusivity increased as the FWHM-1 increased. The highest diffusivity corresponds to 700°C while the lowest to the SHT sample.

The PTR amplitude signal was more sensitive than the PTR phase signal to observe the effect of the PHT temperature on alpha brass thermal, structural, and Vickers microhardness properties.

It is clear that the theoretical results obtained in COMSOL describe temperature variations as a function of the penetration depth of the incident radiation in the material, which in turn depends on factors such as the incident power. Because in the photothermal radiometry technique the thermal wave captured by the detector is translated as amplitude and phase signals, it is not possible to correlate both results. However, it is clear that a finite element analysis such as that offered by COMSOL offers the advantage of inferring the behavior of the variables involved in the process.

Among the possible improvements to the program are the inclusions of the modulation of the light source, which is a very important factor in the photothermal radiometry technique (PTR). The thermal wave generated in the material is very weak and necessarily requires an amplification. Without the modulation of the light source, the amplitude and phase parameters describing the thermal wave would not be possible to capture due to the amount of interference present in the medium. It is important to mention that the modulation frequency of the incident beam directly influences the penetration length in the material and consequently the propagation of the thermal wave.

With a more detailed theoretical**–**experimental analysis, it is possible to arrive at a comparable result between both parties, either by making measurements directly from temperature variations in the samples analyzed or by defining the variables and conditions in the program that allow obtaining the parameters of amplitude and phase of the generated thermal wave.
