Bernardo Hernandez Morales

The lightweight design of 3D-printed polylactic acid (PLA) components requires optimization strategies that reduce material usage while preserving mechanical performance under loading conditions. In this study, cubic lattice topology optimization was applied to tensile and compression specimens manufactured by 3D printing using PLA. The mechanical properties of the base material were experimentally determined and incorporated into finite element analyses. The boundary conditions were defined to reproduce the experimental stress state under standardized testing, with tensile and compressive loads selected based on the material’s yield strength. The optimized geometries were subsequently fabricated by 3D printing and mechanically tested. A qualitative agreement was observed between the simulated and experimental responses, confirming that the gradient-driven optimization approach implemented in ANSYS provided physically representative and experimentally validated designs. The printed PLA exhibited ductile-like behavior attributed to the fused deposition modeling process. Thus, this work demonstrates the feasibility of integrating topology optimization, finite element analysis, and experimental validation to develop PLA components under realistic loading conditions.

Los modelos físicos son una herramienta fundamental en investigación en Ingeniería de Procesos, que no ha sido aprovechada cabalmente para educación en Ingeniería. Un modelo físico es una representación, a escala y usualmente con materiales distintos, de un reactor industrial. En ese sentido, la mayoría de los modelos físicos en Ingeniería Metalúrgica se construyen con acrílico, lo que permite visualizar patrones de flujo, burbujeo y mezclado, entre otras características del sistema. En el contexto del estudio de la Ingeniería de procesos metalúrgicos, es importante cuantificar la transferencia de masa sólido-líquido en reactores tales como el convertidor Peirce-Smith para obtención de mata de cobre, debido a que la disolución de los sólidos que se agregan durante la operación está controlada - principalmente - por el transporte de masa. Sin embargo, es difícil cuantificar esto a partir de las ecuaciones gobernantes de dinámica de fluidos y transporte de masa, debido a los fenómenos complejos que interactúan durante la conversión de mata de cobre dentro del reactor. En lugar de eso, se recurre a la llamada aproximación de intercara, que utiliza al coeficiente de transferencia de masa para caracterizar la rapidez de disolución del sólido. Evidentemente, la determinación experimental de este parámetro es de vital importancia para estudiar al reactor. En este trabajo se reportan resultados obtenidos con un modelo físico del convertidor Peirce-Smith para estimar al coeficiente de transferencia de masa sólido-líquido mediante la medición de la pérdida de peso de cilindros de ácido benzoico sinterizados. Con estos resultados se aseguró que este ejercicio se puede implementar en el laboratorio del curso “Ingeniería de Procesos Metalúrgicos y de Materiales”, por lo que se incorporará al trabajo en el laboratorio. El modelo físico representa una sección del reactor (que es cilíndrico, con una hilera de toberas), simulando solamente a una de las toberas de alimentación de gas; se trata de un reactor que opera intermitentemente (batch). La inyección del aire genera burbujas que forman una “pluma” (zona donde las burbujas se mezclan con el líquido) cuyo movimiento provoca mezclado en el líquido. Para calcular el coeficiente de transferencia de masa se midió la pérdida de peso de un cilindro sólido soluble en agua; el cilindro estaba sumergido dentro del modelo a profundidad constante. Las variables estudiadas fueron el flujo volumínico de aire inyectado (0, 2, 5, 10, 15 y 20 LPM) y la posición de los cilindros (5, 10 y 20 cm, medidos desde la boquilla de alimentación de aire). Además, se realizaron pruebas de adición instantánea de trazador para caracterizar al tiempo de mezclado. El análisis estadístico de los resultados indicó que el flujo volumínico es el factor preponderante, seguido de la posición desde la boquilla y de la combinación de ambos. El trabajo en el laboratorio se ha diseñado para que los estudiantes puedan llegar a esta conclusión a partir de sus propias mediciones y no usando un “receta” para guiar el trabajo en el laboratorio.

This work presents a heat transfer and boiling model that computes the evolution of the temperature field in a representative steel workpiece quenched from 850 or 930 °C by immersion in water flowing at average velocities of 0.2 or 0.6 m/s, respectively. Under these conditions, all three boiling regimes were present during cooling: stable vapor film, nucleate boiling, and single-phase convection. The model was based on the numerical solution of the heat conduction equation coupled to the solution of the energy and momentum equations for water. The mixture phase approach was adopted using the Lee model to compute the rates of water evaporation–condensation. Heat flux at the wall was calculated for all regimes using a single semi-mechanistic model. Therefore, the evolution of boiling regimes at every position on the wall surface was automatically determined. Predictions were validated using laboratory results, namely: (a) videorecording the upward motion of the wetting front along the workpiece wall surface; and (b) cooling curves obtained with embedded thermocouples in the steel probe. Wall heat flux calculations were used to determine the importance of the simultaneous presence of all three boiling regimes on the heat flux distribution. It was found that this simultaneous presence leads to high heat flux variations that should be avoided in production lines. In addition, it was determined that the corresponding inverse heat conduction problem to estimate the active heat transfer boundary condition must be set-up for 2D heat flow.

This work presents a heat transfer and boiling model that computes the evolution of the temperature field in a representative steel workpiece quenched from 850 or 930°C by immersion in water flowing at average velocities of 0.2 or 0.6 m/s, respectively. Under these conditions, all three boiling regimes were present during cooling: stable vapor film, nucleate boiling, and single-phase convection. The model was based on the numerical solution of the heat conduction equation coupled to the solution of the energy and momentum equations for water. The mixture phase approach was adopted using the Lee model to compute the rates of water evaporation-condensation. Heat flux at the wall was calculated for all regimes using a single semi-mechanistic model. Therefore, evolution of boiling regimes at every position on the wall surface was automatically determined. Predictions were validated using laboratory results, namely: a) Videorecording the upward motion of the wetting front along the workpiece wall surface, and b) cooling curves obtained with embedded thermocouples in the steel probe. Wall heat flux calculations were used to determine the importance of the simultaneous presence of all three boiling regimes on the heat flux distribution. It was found that this simultaneous presence leads to high heat flux variations that should be avoided in production lines.

A detailed study at the microscopic level of the transient behavior of boiling phenomena during quenching of an AISI 304 stainless steel, conical-end, cylindrical probe in flowing water at 60 °C was conducted using high-speed video recordings and cooling curve data acquisition. Two free-stream velocities (0.2 and 0.6 m/s) and two initial probe temperatures (850 and 950 °C) were investigated. It was complemented by video recordings at 60 fps to calculate the wetting front velocity. Surface heat flux histories at the thermocouple positions were estimated by solving the corresponding Inverse Heat Conduction Problem. As the water velocity increases the duration of the vapor film at each thermocouple position shortens and the difference among cooling curves at the thermocouple positions decreases. Increasing the initial temperature increases the duration of the vapor film stage. The wetting front velocity increased from 4 to 6 m/s. The time to reach the maximum surface heat flux at the position of the thermocouple closest to the probe tip ranged from 9.7 to 18 s. Undulations at the vapor-liquid interface that appear periodically and propagate in the direction of quenchant flow were observed early during the vapor film stage. Later, before the collapse of the vapor film, a kind of a shock wave was generated at the probe tip which modified the appearance of the film. Once the Leidenfrost temperature is reached, a wetting front (which consists of many small bubbles that coalesce rapidly in a very small area) is formed and travels in the direction of quenchant flow while fewer and larger bubbles nucleate and grow upstream. The nucleation, growth and detachment of the larger bubbles was studied; as the free-stream velocity decreases larger values of bubble maximum diameter and half-life time were observed, while the initial temperature has a marginal effect on these quantities.

International standards for cooling curve analysis use flat-end cylindrical quench probes; however, changing the probe end may lead to a better performance. To assess the effect of probe geometry on the flow near the solid–liquid interface, computational fluid dynamics (CFD) simulations of velocity and pressure fields under low-temperature conditions were carried out. To validate the mathematical model, tests were performed in a laboratory-scale device to visualise streamlines around the probe. The variables studied were probe end geometry (flat-end, hemispherical-end, and conical-end) and water free-stream velocity. From the simulations, it was observed that the flat-end cylindrical probe distorts the flow pattern near the probe end. This distortion agrees with the computed dynamic pressure field, and it is attributed to the decreasing velocity in that region. Streamlines around the conical-end and the hemispherical-end probes suggests more favourable hydrodynamic conditions for cooling curve tests. The measured cooling curves were more reproducible when using the conical-end probe, which may be explained based on variability in the collapse of the vapour film and the advancing of the wetting front. Videos taken during the quench tests showed different initial vapour film geometry, depending on the probe geometry, that can be explained using the computed streamlines.

Cooling curve analysis has emerged as a preferred method to characterize the cooling power of quenching media. This methodology is based on measuring the local cooling curve in a laboratory-scale probe using thermocouples. Several methods have been proposed to analyze cooling curves. Among them, the temperature gradient method (TGM) developed by Professor Liščić uses cooling curves measured at the surface and 1.5 mm below the surface of a cylindrical probe (the Liščić-Nanmac probe) to calculate the surface heat flux during quenching. In this work, we measured the thermal response at a location near the surface of cylindrical probes, fabricated with AISI 304 stainless steel, with two different geometries (conical- and hemispherical-end) during quenching from 850°C with water at 60°C, flowing parallel to the probe’s longitudinal axis. Together with the probe geometry, the experimental matrix included two values of water velocity (0.2 and 0.6 m/s). The data was used to estimate the surface heat flux and thermal response at the probe surface by solving a one-dimensional inverse heat conduction problem (IHCP) without phase change. The TGM was then applied to re-estimate the surface heat flux using the cooling curves at the subsurface (measured) and at the surface (estimated by solving the IHCP). The surface thermal gradient computed solving the IHCP is higher and, therefore, the surface heat flux estimated solving the IHCP is also higher than the value calculated with the TGM. The hemispherical-end probe delays the rupture of the vapor film, producing low values of the surface temperature at the time of maximum heat extraction; this results in extremely high values of the heat-transfer coefficient, which precludes the use of this geometry in conjunction with the TGM. The thermal profiles are parabolic, which restricts the maximum depth at which a subsurface thermocouple may be placed to use the TGM confidently.

Experiments for cooling curve analysis of laboratory-scale quenched probes produce a wetting front that advances at a finite velocity along the longitudinal axis of the probe as cooling progresses. The wetting front velocity depends on probe material and geometry as well as the type of quenchant, its temperature, and agitation. Because of the wetting front, the mathematical model of the direct heat conduction problem to compute the evolution of the thermal field within the probe may be characterized as a moving front boundary problem. In this work, cooling curves at three subsurface locations along the length of conical-end cylindrical probes, fabricated with AISI 304 stainless steel, during quenching from 850°C with water at 60°C flowing parallel to the probe’s longitudinal axis were measured. A fourth thermocouple located at the geometrical center of the probe was used to validate the model. Two values of free-stream water velocity (0.2 and 0.6 m/s) were studied. As a first approximation, the measured cooling curves were used to estimate the corresponding surface heat flux histories by solving three separate 1-D inverse heat conduction problems. Then, the thermal field evolution within the probe was computed by solving a 2-D axis-symmetrical heat transfer model. The boundary condition at the probe surface was modeled with a composite mapping of the surface heat flux histories. The surface heat flux history estimated for the lower section of the cylindrical part of the probe was applied as a boundary condition for the probe tip. It was found that the cooling curve at the lowest thermocouple position was overestimated; thus, the surface heat flux history for the probe tip was divided by 1.2 to correctly model the thermal response. The model was successfully validated by comparing measured and computed cooling curves for the thermocouple located at the probe’s geometrical center.

This article reviews some of the limitations of the standard cooling curve analysis and the Jominy hardenability test in extending the results to actual quenching in industrial setups and reports the development of a new portable tool—Reference QuenchProbe—for estimating cooling rates, hardness, and microstructure distributions in hardenable steel grades during immersion quenching, which can be used by the heat treater in the plant. The specimen is made of the same grade of steel as the quenched component with section thickness matching that of the component, which is a departure from standard laboratory tests. The test is carried out in the plant under actual conditions dispensing the need to correlate the standard cooling curve data and end quench hardenability tests done in the laboratory to industrial practice. To test the suite of mathematical models associated with the Reference QuenchProbe hardware and software, specimens of different grades of steels were instrumented with a single thermocouple near the surface of the specimen. Using the cooling data at the point of measurement, the cooling rates, microstructure, and hardness at other critical locations were computed. An enthalpy-based non-linear inverse heat conduction model was coupled with austenite decomposition models for handling the latent heat liberated during quenching. Several steels ranging from low carbon to medium alloy steels were both end-quenched by water and immersion quenched in several industrial quenchants. The computed hardness of end quenched and immersion quenched specimens were shown to be in good agreement with the measured values. The Reference QuenchProbe is thus shown to generate data needed for heat treatment process design including quenchant selection, which can be directly used in practice.

Mathematical modeling is a powerful tool to design, control and optimize heat-treating processes. However, the complex interactions occurring between the thermal, microstructural, and stress fields inside the part during those processes (which must be taken into account in detailed modeling work) precludes its use in many instances—especially in a production environment. Thus, it is desirable to find methodologies that can speed up the simulations while maintaining the mathematical model close to reality. In this work, the evolution of the microstructural field was estimated from fraction-transformed-temperature correlations derived directly from a published continuous-cooling-transformation (CCT) diagram, which uses the cooling rate at 750°C as the x-axis. This approach “softens” the coupling between the thermal and fraction-transformed fields resulting in an efficient algorithm. The thermal field evolution was computed using standard procedures embedded in the commercially available code Abaqus, whereas empirical equations describing the fraction transformed-temperature relationships were programmed through user subroutines. The mathematical model was validated by comparing measured and model-predicted thermal response and final microstructure. In the experiments, austenitized AISI 4140 steel cylindrical probes (0.5-in. diameter × 2-in. length) were cooled in: (1) still air, and (2) a fluidized bed reactor, both at room temperature. The thermal response was measured during the cooling process by inserting two thermocouples: one at the geometrical center of the probe and the other near the probe surface, at mid-length. The latter was input to a code developed in-house to estimate the surface heat flux history, which constitutes the active boundary condition for the direct heat conduction problem and was, in turn, fed to the computational model. Once heat treated, the probes were prepared for metallographic observation using standard techniques. The results indicate that the proposed methodology can be used for predicting the thermo-microstructural evolution during a heat-treating process.