1. Introdução à dilatação térmica e fluência em metais

Every structure is subjected to different types of load, which it is up to the designer to take into account correctly when designing the equipment. Gravitational loads, wind loads and overloads are some typical examples of stresses on structures and equipment. In addition to these loads, thermal loads are extremely important for Structural Integrity, since they impose internal stresses on the elements to counteract the thermal expansion they undergo.

In general, structures exposed to the weather and built in regions with normal climatic conditions (conveyors, buildings, yard machinery, etc.) are subject to temperature variations throughout their lives of around 20°C. For places with extreme climatic conditions, higher values can be reached, such as in the Gobi desert, where in summer the temperature reaches 45°C and in winter -40°C. To calculate the change in linear length of a body due to the action of temperature, the following formula is used:

 

Thermal expansion is converted into internal stress in an element if the deformation is restricted by the external environment. Take the example in Figure 1, which shows the same beam with two different boundary conditions. The beam on the left, simply supported, expands uniformly without changing shape when heated from 20°C to 100°C. In this condition, no forces against the movement of the structure are generated due to thermal expansion, and the stress resulting from the thermal load is negligible. In the beam on the right, which is bi-span, thermal expansion is restricted by the support, resulting in forces against expansion, thus changing the shape and generating stresses in the structure. This simple example depicts the general consideration of temperature effects on structural design. Figure 2 shows the deformation of a railroad track when subjected to temperature variation.

Figure 1: Reactions and deformations of a simply supported beam (left) and a doubly braced beam (right) when heated.

Figure 2: Axially constrained rail deformed due to thermal expansion.

 

2. Como a temperatura afeta as tensões internas

Thermo-structural analysis is carried out to evaluate the influence of the thermal load on the deformations and, consequently, on the stresses. Using the finite element method, there are two ways of considering this interaction: weak and strong thermo-structural coupling. Weak coupling consists of carrying out a thermal analysis to determine the temperature field and using this data as input into the structural model, without changing one parameter influencing the other. Strong coupling, on the other hand, solves the equations concurrently, taking into account the interaction between the solutions (see an example of coupling between phenomena in the FSI article).

 

3. Métodos de análise termo-estrutural (FEM)

The most common way of carrying out thermo-structural analysis is by means of weak coupling, as it has lower computational costs and minimal differences for most engineering problems.

In addition to the stresses generated by thermal expansion reactions, there are other important effects to consider during design. This article will look at the concepts of creep, the ways of considering this effect in structural strength and a case study that illustrates the importance of considering creep in the structural safety of a chimney.

 

4. Fluência: estágios e impactos na integridade estrutural

Creep in metals is a phenomenon that occurs when a material is subjected to constant stress and continues to deform over time. Imagine a bi-supported beam supporting the weight of an engine. If the beam is at room temperature (20°C to 40°C), it will deform when the motor is placed on it and then remain static with constant deformation. If this same beam is subjected to a temperature of 500°C, depending on the level of stress it will continue to deform and may collapse.

Creep occurs more quickly at high temperatures, such as in aircraft engines or turbines, where the metal parts are under intense heat and stress simultaneously. Over time, this deformation can affect the integrity of the material, a factor that must be taken into account during design.

The phenomenon is characterized by three stages: the first is transient, in which the structure deforms due to external loads and partly due to the creep effect; the second is a stationary and constant deformation; finally, the third stage is unstable and can culminate in the rupture of the material. Figure 3 shows the typical scheme for creep tests and the three phases explained.

Figure 3: Diagram of a typical creep test, illustrating the three stages of deformation observed in the specimen. SOURCE: Adapted from Dowling - 2013.

"Creep deformation in metallic materials becomes significant at temperatures above the range of 30 to 60% of the material's melting temperature" - Dowling - 2013. Creep analysis can be considered in different ways. The most simplified approach used for designing structures subjected to fire is to reduce the modulus of elasticity and the resistant stress as a function of the acting temperature. This approach, however, is not capable of predicting the amount of plastic deformation due to creep of the material as a function of exposure time. For this, there are empirical methods that consider the acting stresses and time by means of equations that define the material's resistance as a function of time, as well as rheological models that study the material's micromechanics. Figure 4 shows the modulus of elasticity and yield stress curves as a function of temperature, which are commonly used in the simplified evaluation.

Figura 4: Redução da tensão de escoamento e do módulo de elasticidade em função da temperatura atuante.
FONTE: Adaptado de EN-1993-1-2.

5. Estudo de caso: chaminé metálica sob altas temperaturas

Metal chimneys are subjected to high temperatures from contact with the gases coming out of the furnaces. In general, refractories and insulators are used to reduce the temperature acting on the side and maintain the integrity of the equipment. However, there are processes in which the use of refractory is not recommended due to the difficulty of maintenance, the risk of detachment, contamination of the metal produced and even accidents. Therefore, some chimneys are built with the side in direct contact with the gas.

In a recent study carried out by Kot Engenharia, a set of metal chimneys compromised by excessive deformation of the entire side was analyzed. In order to assess the causes of the failures and propose solutions, the work was divided into four stages:

• Field inspection to detect non-conformities and design changes;
• Temperature measurement with thermographic camera;
• Análise estrutural por elementos finitos (estática, flambagem, fadiga, não linear {fluência}) e proposição de soluções;
• Monitoring temperatures in newer chimneys to correlate with existing sensors and determine safe operating limits.

5.1. Inspeção

During the inspection, deformations were observed throughout the base of the side. To contain the advance of the deformations, a secondary support tower had already been installed to bypass the compressive loading in the area. Figure 5 shows the deformed structure and the shoring tower installed.

Figure 5: Deformation in the side wall of chimneys with external support structure installed for redundancy and to reduce the risk of structural collapse.

In addition to the deformations, design changes were observed that increased the chimney's blocking, see Figure 6. As illustrated in Figure 1, structures subjected to temperature and with greater containment are more stressed and generally have higher tensions. These design changes were taken into account in the computer model to assess the causes of equipment failure. Other non-conformities were identified and solutions were proposed to ensure the integrity of the asset.

Figure 6: Changes to the expansion joints and sliding supports identified during the field visit.

5.2. Medição termográfica para definição do perfil térmico

Thermography is an imaging technique used to obtain the temperature profile of a radiating body. The camera uses sensors to detect and map the infrared radiation emitted by objects or surfaces. Image conversion takes place by calibrating the emissivity parameters of the material, which are defined by the state of the surface and vary as a function of temperature. Therefore, based on the measurements taken, the emissivities of the material were calibrated in order to build the thermal profile of the chimneys.

After the measurements and based on the gas temperature records from the company's thermocouples, it could be seen that the three chimneys had different temperatures, which varied throughout the day. Therefore, various combinations of temperature distribution between the chimneys were evaluated, following the recording trend of some days of operation.

Figure 7 shows one of the thermographic images captured, while Figure 8 shows the temperature distribution between the chimneys. In addition to the temperature loads, other actions were considered to determine the load combinations evaluated.

Figure 7: Thermography carried out to determine the temperature profile.

Figure 8: Temperature distribution in the chimneys for one of the loading cases evaluated.

5.3. Análise estrutural por elementos finitos

In order to characterize the failures and propose reinforcements, various hypothesis tests were carried out and different analyses performed. The static evaluations indicated failures in some areas of the equipment due to the temperature difference, which resulted in different deformations due to thermal expansion, increasing the acting stresses. In addition, there were regions susceptible to cracking, as can be seen in Figure 9. It is important to note that the most critical regions identified in the study were in fact damaged in the field.

Figure 9: Results of the fatigue analysis, indicating that the useful life of the welds is less than the asset's operating time - highlighting the cracks in the region observed in the field.

Linear buckling analyses and non-linear creep analyses were carried out to characterize the central problem, which was the permanent deformation of the side, since the chimney reached temperatures above 450°C and could reach values close to 620°C, which are critical for the effects of creep deformation.

The analyses carried out identified that the side was at risk of buckling when operating above certain temperatures, as shown in Figure 11. In addition, the non-linear creep analysis showed that operating the chimney at high temperatures for longer than two hours resulted in permanent plastic deformations exceeding the limits allowed by law, as can be seen in Figure 10.

Figure 10: Results of the non-linear creep analysis.

Figure 11: Buckling analysis identifying the risk of buckling on the chimney side.

5.4. Intervenções propostas e refeorços estruturais

After identifying the problems that caused the structure to fail, the process of proposing reinforcements and improvements began. This stage included some particularities of the process that had to be met, such as: allowing operation up to a certain temperature, not using refractories to facilitate maintenance, reducing the risk of contamination of the material produced and carrying out an assessment to obtain the solution with the least possible economic impact and ease of installation.

As a result, changes were proposed to the material, geometry, improved welds and altered connections to allow the structure to expand. With the proposed reinforcements, it was possible to increase the fatigue life of the most critical welds by 350%, adapt the structure to the buckling resistance requirements for the entire operating temperature range and allow the new chimney to operate at temperatures of 600°C for periods of up to 10 hours, improving process control and guaranteeing the safety and operational integrity of the structure. The following figures exemplify the proposed modifications (Figure 12) and the results of the analysis considering the implementation of the reinforcements (Figure 13).

Figure 12: Example of a proposed modification to improve the structure's thermal expansion.

Figure 13: Comparative results of the static analysis before and after implementation of the reinforcements.

5.5. Monitoramento contínuo com termopares para elaboração de controles da operação

As the material's resistance is dependent on the operating temperature, it was necessary to establish safe operating limits, as the materials have physical resistance limits (see Figure 4). Continuous monitoring was therefore carried out using thermocouples welded to the side structure, in order to determine a correlation between the gas measurement sensor and the side temperature. This correspondence has allowed the client to work under safe operating conditions at all times.

Figure 14: Continuous temperature instrumentation in the chimney for process control.

6. Conclusões e aprendizados

After the detailed study carried out by Kot, it was observed that the chimney failures were related to changes in the support conditions of the ducts and, above all, to the high operating temperatures. The results of the buckling and non-linear creep analyses assertively represented the state of deformation verified in the field, indicating that the models built are faithful to reality.

With the proposed modifications to the geometry and the indication of safe operating ranges, it was possible to design a structure suitable for operation and within the reality of the installation and costs targeted by the client. This work shows the importance of understanding the physical phenomena involved and the assertiveness achieved through the correct use of the finite element method, both in characterizing the failure aspects and in proposing simpler and more efficient reinforcements and adjustments.

 

7. Análise de elementos finitos é com a Kot Engenharia

Se você, assim como nossos mais de 150 clientes, busca soluções especializadas em análise estrutural ou prevenção de falhas como deformações, vibrações e corrosão, consulte nossa equipe e conte com a Kot Engenharia. 

Desde 1993, oferecemos serviços de consultoria em engenharia por meio de estudos técnicos com o uso de ensaios não destrutivos, instrumentação de campo e simulações computacionais (FEM, DEM e CFD) para diagnósticos de alta complexidade em estruturas de concreto, metálicas e equipamentos industriais. 

Siga, também, nossas páginas no LinkedIn, Facebook e Instagram para continuar acompanhando nossos conteúdos.