Arrhenius Constitutive Model Research Articles

Predictive Modeling and Optimization of Hot Forging Parameters for AISI 1045 Ball Joints Using Taguchi Methodology and Finite Element Analysis

This study focused on optimizing the hot forging process for AISI 1045 medium carbon steel ball joints, which is crucial for enhancing both their mechanical properties and production efficiency. Traditional hot forging processes often face challenges due to variations in flow stress and microstructural outcomes, which can result in a suboptimal product performance. To address these challenges, this research employed the Taguchi method in conjunction with a finite element (FE) simulation to identify the optimal forging parameters. The Arrhenius constitutive model, based on the Zener–Hollomon parameter, was applied to predict the flow stress with a high level of accuracy, achieving a coefficient of determination (R2) of 0.968 and an average absolute relative error (AARE) of 7.079%. An analysis of variance (ANOVA), a statistical innovation that partitions the total variation into components linked to key process factors, was utilized to determine the significance of these parameters. The ANOVA revealed that the billet temperature played a significant role in influencing the preforming force, finishing force, and mean stress, with a maximum impact of 62.30%, 59.50%, and 94.20% on the variation in the response variable, respectively. Additionally, the friction factor significantly affected the preforming and finishing forces, contributing 36.19% and 38.28%. The validation of the model through both simulations and practical experiments is a testament to the reliability of this research, demonstrating the accuracy of the model with minimal discrepancies in the forging forces and exhibiting errors of just 2.88% and 3.40%. Furthermore, microstructure modeling successfully predicted the key outcomes, such as the grain size and pearlite volume fraction, validating the effectiveness of the simulation in forecasting microstructural characteristics.

A comparative study of hot tensile deformation behavior of 6016 aluminum alloy under LSTM neural network and Arrhenius model

Abstract The isothermal tensile test of 6016-T6 aluminum alloy was carried out on Gleeble-3500 at the temperature range of 400 °C–550 °C and the strain rate range of 0.01–10 s−1. The results show that the thermal deformation mechanism of 6016-T6 is dynamic recovery and dynamic recrystallization. In this paper, the phenomenological Arrhenius constitutive model and the data-driven WOA-LSTM constitutive model for predicting the hot tensile deformation behavior of 6016-T6 aluminum alloy were studied in contrast. The whale optimization algorithm was used to optimize the hyperparameters of LSTM neural network to improve the prediction accuracy of flow stress. The optimization results show that the optimal hidden layer node, maximum training period, initial learning rate and mini batch size of WOA-LSTM are 46, 260, 0.0248 and 16, respectively. In addition, the influence of the number of hidden layers on the results of the network was discussed. The appropriate hidden layer of the network was determined to be 2. The result show that the prediction accuracy of WOA-LSTM constitutive model is better than the Arrhenius constitutive model. The mean absolute error and correlation coefficient are 0.9348% and 0.99952, respectively. Among them, in this study, the Arrhenius constitutive model has low precision and only has high precision within a single temperature range.

Simulation of recrystallization grain growth in AZ61 magnesium alloy based on GA and 3D CA

In this paper, the Arrhenius constitutive model (GA-Arrhenius) optimized by genetic algorithm (GA) is established, and the dynamic recrystallization (DRX) grain growth process of AZ61 magnesium alloy during hot deformation is simulated by three-dimensional cellular automata (3D CA), and the morphological evolution and grain boundary migration of recrystallized grains are reproduced. The results show that the GA-Arrhenius model accurately predicts the rheological behavior of the material, while the 3D CA model effectively describes the formation and growth mechanism of grains during DRX.

Microstructure evolution and constitutive modeling of Cu-bearing high-strength low-alloy steel during hot deformation

The microstructural evolution of austenite during hot deformation determines the mechanical properties of steel products. Consequently, industrial applications necessitate a thorough comprehension and modeling of this process. Under varied hot deformation conditions, the flow stress, microstructure evolution, and constitutive modeling of a Cu-bearing steel were examined. At various temperatures and strain rates, compression experiments are conducted, and the resulting microstructures were studied by electron backscatter diffraction (EBSD). Our results indicate that fine prior austenite grains with an average diameter of 22.1 m and a high-angle grain boundary density of 0.25 m1 were produced at a deformation temperature of 950 °C and a strain rate of 1 s−1. The dominating rotating cube components ({001}<110>) in the sample deformed at 1150 °C were gradually replaced by the γ-fiber texture component as the deformation temperature decreased. To accurately predict the flow behavior of this steel, we proposed an improved Arrhenius constitutive model that accounts for strain rate and adiabatic temperature rise. With a correlation coefficient (Rc) of 0.9936, a root mean square error (RMSE) of 4.92%, and a relative error (δ) of 6.05 MPa, our results demonstrate that this model predicts the flow stress of the experimental steel with good precision. This research contributes to the development of high-performance steel products by shedding light on the microstructural evolution and flow behavior of Cu-containing steels under hot deformation conditions.

An Optimized Strain-Compensated Arrhenius Constitutive Model of GH4169 Superalloy Based on Hot Compression.

A precise constitutive model is essential for capturing the deformation characteristics of the GH4169 superalloy in numerical simulations of thermal plastic forming processes. Hence, the aim of this study was to develop a precise modified constitutive model to describe the hot deformation behavior exhibited by the GH4169 superalloy. The isothermal cylindrical uniaxial compression tests of the GH4169 superalloy were carried out at temperatures of 950~1100 °C and strain rates of 0.01~10 s-1 using a Thermecmastor-200KN thermal-mechanical simulator. The original strain-stress curves were corrected by minimizing the effects of plastic heat and interfacial friction. Based on the true stress-strain curves, the original strain-compensated Arrhenius constitutive model was constructed using polynomial orders of 3, 5, and 10, respectively. The results showed that once the polynomial order exceeds the 5th, further increasing the order has little contribution to the accuracy of the model. To improve prediction ability, a higher precision Arrhenius constitutive model was established by extending a series of material parameters as functions that depend on temperature, strain, and strain rate, in which the error can be reduced from 4.767% to 0.901% compared with the classic strain-compensated Arrhenius constitutive model.

Hot deformation mechanism of a rapidly-solidified Al–Zn–Mg–Cu–Zr alloy

This study systematically investigates the flow behavior of 7050 aluminum (Al) alloy produced via spray forming and subjected to a proposed pretreatment through thermal compression tests. The experimental findings reveal that the peak stress increased with decreasing deformation temperature or increasing strain rates. The parameters in the Arrhenius constitutive model were determined and verified by experimental results for spray formed (SFed) 7050 Al alloy. Hot deformation activation energy of the SFed 7050 Al alloy (147.38 kJ/mol) is notably lower than that of cast Al–Zn–Mg–Cu–Zr alloys, which is attributed to factors such as fine grains, low segregation, pores, and dispersed Al3Zr induced by pretreatment. Furthermore, processing maps have been constructed at various strains, revealing optimal stable deformation conditions at 300–450 °C/0.001–0.15s−1 and 425–450 °C/0.2–1s−1. Microstructural analysis of deformed samples highlights the critical role of dynamic recrystallization in influencing the stable and unstable areas of the alloy, which may be activated by high temperature and slow strain rate. The hot deformation mechanism of the SFed Al alloy is governed by interactions among η-Mg(Zn,Al,Cu)2 precipitates, dispersed Al3Zr particles, dislocation structures, and (sub-)grain boundaries.

Hot compression deformation behavior and microstructure evolution of Al-0.5Mg-0.4Si alloy

The hot compression tests for as-cast Al-0.5Mg-0.4Si alloy were performed on Gleeble-3500 thermo-mechanical simulator under temperatures of 350–500 °C and strain rates of 0.01–10 s−1. Based on the experimental data, a strain-compensated Arrhenius constitutive model was established by exponential function coupling strain. The hot processing map of Al-0.5Mg-0.4Si alloy was established, and the reasonable processing parameters were obtained. The microstructural evolution and dynamic softening mechanisms of the alloy were analyzed using electron backscatter diffraction (EBSD). A detailed description of the evolution of dislocation and the dislocation density during the deformation process was provided. The results indicate that the softening mechanisms of Al-0.5Mg-0.4Si alloy are dynamic recovery (DRV) and continuous dynamic recrystallization (CDRX). The dynamic recovery mechanism is related to the cross slip of the screw dislocation. High temperature and low strain rate are conducive the occurrence of CDRX. This study provides comprehensive guidance for the hot processing of Al-0.5Mg-0.4Si alloy from both macroscopic and microscopic perspectives.

Investigation of the Hot Deformation Behavior of 22Cr‐25Ni Austenitic Heat‐Resistant Steel by Combining Constitutive Model and Processing Map

The hot deformation behavior of 22Cr‐25Ni austenitic heat‐resistant steel at the temperatures of 950–1150 °C and strain rates of 0.01–10 s−1 is studied by isothermal compression test. It is found that the dynamic recrystallization (DRX) degree of the steel increases with the increase of temperature. The DRX degree decreases with the increase of the strain rate from 0.01 to 1 s−1, whereas the DRX degree increases with the increase of the strain rate from 1 to 10 s−1. The hot deformation activation energy is as high as 624.25 kJ mol−1 due to the addition of a large number of alloying elements. The typical strain compensation Arrhenius constitutive model established can be used to roughly predict the hot flow behavior of the steel. Furthermore, a modified model considering the influence of strain rate and deformation heat on the deformation process is proposed and showed higher accuracy (statistical parameters r = 0.994 and average absolute relative error = 4.59%). The DRX zone of the steel is determined to be 1080–1150 °C/0.01–0.1 s−1 through processing map analysis, representing the appropriate hot working zone. The microstructure corresponding to the instability zone in the processing map exhibits deformation concentration bands or necklace structures.

Exploring microstructure evolution and machine-learning methods based on SCAT-CIWOA-BP-DMM theory during hot deformation of 56Ni–32Ti–12Hf alloy

Hot compression simulation tests were carried out on a 56Ni–32Ti–12Hf alloy at temperatures ranging from 800 to 1000 °C and strain rates ranging from 0.001 to 1 s−1. The study aimed to explore the hot deformation behavior and microstructure evolution mechanism of the alloy. Two flow stress prediction models were developed: a strain-compensated Arrhenius constitutive (SCAT) model based on phenomenology and a chaotic mapping adaptive inertia weight whale optimization algorithm-optimized back propagation neural network (CIWOA-BPNN) model based on machine learning. In comparison to the SCAT model, the CIWOA-BPNN model demonstrates higher prediction accuracy, improved error correlation coefficient, decreased average relative error, and lower root mean square error and mean absolute error. The hot processing map of the 56Ni–32Ti–12Hf alloy was developed using dynamic material modeling (DMM) theory and flow stress data predicted by the CIWOA-BPNN model. The optimal hot processing range was found to be between temperatures of 875–975 °C and strain rates of 0.001–1 s−1. The study found that within the optimal processing interval, the softening mechanisms observed were discontinuous dynamic recrystallization (DDRX) and continuous dynamic recrystallization (CDRX). An increase in power dissipation efficiency (η) led to an increase in the dynamic recrystallization (DRX) fraction from 27.1 % to 41.9 %, while the substructure fraction decreased from 34.2 % to 19.8 %. The decrease in the number of dislocations around the DDRX grains further validated the accuracy of the identified optimum machining interval in this research.

Hot deformation behavior and processing map of vanadium particles reinforced AZ31 composite

The vanadium particles reinforced AZ31 matrix composite (VP/AZ31) was prepared using the powder metallurgy method. Subsequently, hot deformation behavior of VP/AZ31 composite was studied through hot compression trials. The experimental parameters were set in a temperature range of 250–400 °C and a strain rate range of 0.001–1 s−1. Based on the experimental results, a strain-compensated Arrhenius constitutive model was developed to accurately forecast the flow behavior of VP/AZ31 composite. Moreover, the thermal activation energy was calculated to be 138.605 kJ/mol and the processing map was delineated according to the dynamic material model theory. The processing map revealed that the optimal processing area existed under 363–400 °C/0.001–0.004 s−1, where the efficiency of power dissipation exceeded 23 %. Notably, the highest efficiency of power dissipation occurred at 400 °C/1 s−1, which exceeded 30 %. Under these conditions, dynamic recrystallization (DRX) was sufficiently developed, indicating the enhancement of workability. It is estimated that the instability region for VP/AZ31 composites occurred within the conditions of 250–325 °C/0.16–1 s−1, characterized by crack formation. The DRX of VP/AZ31 composite is predominantly governed through the mechanism of discontinuous DRX (DDRX).

Constitutive Model and Microstructure Evolution of Ti65 Titanium Alloy.

The hot deformation behavior and mechanism of Ti65 alloy with a bimodal microstructure were investigated by isothermal compression experiments conducted on the Thermecmastor-Z simulator equipment at temperatures ranging from 950 to 1110 °C and strain rates ranging from 0.01 to 10.0 s-1. The Arrhenius constitutive model, based on strain compensation, and Grey Wolf optimization-neural network with back propagation model (GWO-BP), were both established. The differences between the experimental and predicted value of flow stress were compared and analyzed using the two models. The results show that the prediction accuracy of GWO-BP in the two-phase region is higher than that of Arrhenius model. In the single-phase region, both methods demonstrated high prediction accuracy. Compared to the single-phase region, the flow stress of Ti65 alloy shows a higher degree of softening in the two-phase region. During deformation in the two-phase region, the initial lamellar α phase transformed from a kinked and elongated morphology to a globularized topography as the strain rate decreased. Boundary-splitting was the primary mechanism leading to the spheroidization process. The degree of recrystallization increased with the increase in strain rate during the deformation in the single-phase region, while dynamic recovery and strain-induced grain boundary migration were the main deformation mechanisms at a lower strain rate. Discontinuous dynamic recrystallization may be the dominant recrystallization mechanism under a high strain rate of 10 s-1.

Hot deformation behavior of a layered heterogeneous microstructure TiAl alloy prepared by selective electron beam melting

TiAl-based alloys are known for their exceptional high-temperature properties but suffer from low hot workability. The emergence of additive manufacturing (AM) technology significantly decreases the workability requirement, while the microstructure heterogeneities in AMed TiAl are troublesome. This paper explores the hot deformation behavior and microstructure evolution of a layered heterogeneous microstructure TiAl alloy prepared by selective electron beam melting. The Arrhenius constitutive model with strain compensation was established, and hot processing maps were constructed. The microstructure showed that at the initial stage of deformation, a large number of dislocation slips occur preferentially in the soft coarse-grained layers. With the increase of strain, dislocation accumulation in heterogeneous interfaces, and dynamic recrystallization (DRX) occurs. Eventually, the coarse-grained region is constantly occupied by fine DRX grains. A high density of deformation twins at high strain rates further promotes the formation of tiny DRX grains. When the hot compression temperature reaches 1200 °C, the initial alternative fine-grained and coarse-grained hetero-structure transforms into duplex (DP) and near-lamellar (NL) microstructure, and microstructure heterogeneity is eliminated. The results enhance understanding of the hot deformation behavior of heterogeneous microstructure TiAl alloys.

Study on the hot deformation behavior and microstructure evolution of as-forged GH3625 alloy

GH3625 alloy is widely used in aviation, nuclear power and other fields of hot section components. However, the high alloying level, significant deformation resistance, and narrow hot working window of the alloy bring great challenge to the plastic deformation of the alloy. The hot deformation behavior and microstructure evolution of as-forged GH3625 alloy were studied by hot compression tests with deformation temperatures of 930–1180 °C, strain rates of 0.001–1 s−1 and true strain of 0.92. The results show that the flow stress of the alloy exhibits noticeable characteristics of temperature-negative sensitivity and rate-positive sensitivity. The true stress-strain curves are of two types: dynamic recovery (DRV) and dynamic recrystallization (DRX). The strain-compensated Arrhenius constitutive model was used to predict the alloy's flow behavior, with a linear fitting correlation coefficient (R) of 0.9872 and an average relative error (AARE) of 8.92%. The hot processing map of the alloy based on Prasad was constructed and superimposed. It was found that there were two instability regions, which were located in the low temperature and high strain rate region and the high temperature and low strain rate region respectively. The optimal processing region was 1154∼1180 °C/0.75–1 s−1 combined with the true stress-strain curves and the microstructure. Continuous dynamic recrystallization (CDRX) at subgrains rotation and discontinuous dynamic recrystallization (DDRX) at grain boundaries were identified during thermal deformation. As the η value decreases, the dynamic recrystallization grain size decreases under the deformation condition of 930–1180 °C/1 s−1, and the microstructure evolution mechanism changes from DDRX→ DDRX + CDRX→ DDRX + CDRX + DRV → CDRX + DRV, and ∑3 TBs also reduces.

Processing Maps and Optimized Plastic Behavior Model of TC4 Titanium Alloy Diffusion Bonded Joint at α+β Region Temperatures

The hot processing maps and optimized Arrhenius constitutive model of the TC4 diffusion bonded joint were investigated based on high temperature tensile tests in the temperature range of 1024–1174 K and strain rate range of 0.0001–0.1 s–1. The optimal hot processing parameter in the tensile deformation mode was 0.0001–0.001 s–1/1124 K and 0.0001–0.1 s–1/1174 K, respectively, when the true strain was 0.2. A modified strain compensated Arrhenius-type constitutive model of the joint by combining the evolutionary algorithm and generalized reduced gradient was established. The values of correlation coefficient and average absolute relative error were 0.989 and 7.29%, respectively, indicating the good prediction capabilities.

Effects of C and Al Alloying on Constitutive Model Parameters and Hot Deformation Behavior of Medium-Mn Steels.

Single-pass isothermal hot compression tests on four medium-Mn steels with different C and Al contents were conducted using a Gleeble-3500 thermal simulation machine at varying deformation temperatures (900-1150 °C) and strain rates (0.01-5 s-1). Based on friction correction theory, the friction of the test stress-strain data was corrected. On this basis, the Arrhenius constitutive model of experimental steels considering Al content and strain compensation and hot processing maps of different experimental steels at a strain of 0.9 were established. Moreover, the effects of C and Al contents on constitutive model parameters and hot processing performance were analyzed. The results revealed that the increase in C content changed the trend of the thermal deformation activation energy Q with the true strain. The Q value of 2C7Mn3Al increased by about 50 KJ/mol compared with 7Mn3Al at a true strain greater than 0.4. In contrast, increasing the Al content from 0 to 1.14 wt.% decreased the activation energy of thermal deformation in the true strain range of 0.4-0.9. Continuing to increase to 3.30 wt.% increased the Q of 7Mn3Al over 7Mn by about 65 KJ/mol over the full strain range. In comparison, 7Mn1Al exhibited the best hot processing performance under the deformation temperature of 975-1125 °C and strain rate of 0.2-5 s-1. This is due to the addition of C element reduces the δ-ferrite volume fraction, which leads to the precipitation of κ-carbides and causes the formation of microcracks; an increase in Al content from 0 to 1.14 wt.% reduces the austenite stability and improves the hot workability, but a continued increase in the content up to 3.30 wt.% results in the emergence of δ-ferrite in the microstructure, which slows down the austenite DRX and not conducive to the hot processing performance.

Study on Hot Deformation Behavior and Dynamic Recrystallization Mechanism of Cu‐Ti‐Fe Alloy

Hot compression experiments with the deformation temperatures of 750–950 °C and the strain rates of 0.01–10 s−1 are carried out on a Gleeble‐3500 thermal‐mechanical simulator. The flow behavior and dynamic recrystallization (DRX) mechanism of the Cu‐Ti‐Fe alloy are systematically studied under different hot deformation conditions. According to the curves of flow stress and work hardening rate, the DRX critical condition of the alloy is obtained, and the critical stress value of DRX is small under high‐temperature and low‐strain rate. After fitting, the logarithmic values of the critical stress and critical strain have a linear relationship with lnZ, which indicates that the alloy is more prone to DRX at high temperatures and low‐strain rates. The Arrhenius constitutive model of the alloy is established, the linear correlation coefficient (R2) is 0.984. Combined with the microstructure of Cu‐Ti‐Fe alloy, the microstructure evolution characteristics and DRX mechanism are elucidated. The dominant mechanism of the alloy under the deformation temperature of 750–950 °C is the DRX mechanism. The low‐angle grain boundaries (LAGBs) transform into high‐angle grain boundaries (HAGBs) and continuous dynamic recrystallization (CDRX) grains form. Abundant dislocations gather near the HAGBs, causing grain boundaries to protrude. High‐temperature conditions make the dislocations disappear, forming discontinuous dynamic recrystallization (DDRX) grains.

Hot Deformation Behavior and Processing Maps of 26CrMo7S Steel Used in Oil Exploration.

The hot deformation behavior and flow stress characteristics of experimental 26CrMo7S steel were analyzed using a thermal simulator under a range of conditions, including a strain rate range of 0.01~10 s-1, a temperature range of 850~1250 °C, and a maximum deformation amount of 70%. The Arrhenius constitutive model was built for the corresponding conditions, and the model's accuracy was verified through error analysis. Additionally, hot processing maps were constructed to analyze the processing zone of the steel under different hot deformation conditions. Finally, the microstructure of the processing zones was observed and verified using the electron backscattered diffraction (EBSD). The results indicate that the interaction of work hardening and dynamic softening influences the hot deformation behavior of 26CrMo7S steel. The Arrhenius constitutive equation with a value of the correlation coefficient (r = 0.99523) accurately predicts the flow behavior of 26CrMo7S steel under different strains. The optimal processing zone obtained with the hot processing maps is within a deformation range of 1010~1190 °C and a strain rate range of 0.01~10-1.5 s-1, and the obtained microstructure is in good agreement with the analysis results.

Hot deformation behavior and microstructure evolution model of 7055 aluminum alloy

Hot compression tests were conducted on 7055 aluminum alloy under different strain rates, temperatures, and reduction ratios. The influence of deformation parameters on microstructure evolution and hot deformation behavior was studied through EBSD and TEM characterization. An Arrhenius constitutive model was established and the recovery and recrystallization characteristics of the alloy under different conditions were analyzed. Results showed that the softening mechanism during the hot compression process of 7055 aluminum alloy was mainly attributed to recovery and partial recrystallization. The Zener-Holloman (Z) parameter was utilized to reveal the combined effects of strain rate and temperature on recrystallization behavior. Under conditions of high LnZ values (20 < LnZ), the alloy exhibited predominantly discontinuous dynamic recrystallization (DDRX) characteristics, while at low LnZ values (14 < LnZ <17), it displayed significant continuous dynamic recrystallization (CDRX) characteristics. The alloy showed a coexistence of CDRX and DDRX phenomena under conditions of moderate LnZ values (17<LnZ <20). In addition, based on the characterization, statistical analysis, and examination of the hot-compressed microstructure of the 7055 aluminum alloy, models for recrystallization fraction, grain size evolution, and deformed grain size were established, and an average grain size model was further developed. Comparison between the finite element simulation results based on the models and experimental results demonstrated good agreement in predicting the average grain size.

Arrhenius constitutive equation and artificial neural network model of flow stress in hot deformation of offshore steel with high strength and toughness

ABSTRACT In this study, the thermal deformation behaviour of a high strength offshore steel at different temperatures and rates was investigated through thermal compression experiments.An Arrhenius constitutive model and a back propagation artificial neural network (BP-ANN) were established to address more complex deformation characteristics. The performances of both models were was evaluated using standard statistical parameters such as the correlation coefficient (R) and average absolute relative error (AARE). The results showed that both models can accurately predict the rheological stresses generated during deformation.The BP-ANN outperforms the Arrhenius equation model with correlation coefficients of fit greater than 99.9% and less than 0.8% relative error. At a strain rate of 0.01 s−1 and 10 s−1, the accuracy of the ANN decreases slightly due to the fact that it exceeds the strain rate range of the training set, as compared to the Arrhenius constitutive equations as these are more accurately predicted.

Investigation on hot deformation behavior and quenching precipitation mechanism of 2195 Al-Li alloy

Al-Li alloys suffer from a narrow processing window. The hot deformation behavior of the ramp heating homogenized 2195 Al-Li alloy was investigated by hot compression test in the temperature range of 300–500 °C and strain rate range of 0.01–10 s−1, and the strain compensated Arrhenius constitutive relationship model and processing map of the alloy were established. The laws of Zener-Hollomon parameters on the age-hardening response and quenching sensitivity of the deformed alloy were analyzed. The quenching precipitation mechanism of the deformed alloy were revealed. The results showed that the hardness of the aged alloy tends to increase first and then decrease with increasing Z parameter, while the quenching sensitivity tends to decrease first and then increase. The quench-induced phases are precipitated under the induction of incoherent Al3Zr dispersoids within recrystallized grains. The boundary angle would affect the quenching precipitation behavior. It was also found that the types and amounts of second phases are significantly different between the homogenized and hot-deformed samples under slow cooling rate. The ramp heating homogenized 2195 Al-Li alloy after hot deformation at temperatures of 455–500 °C and strain rates below 1 s−1 possesses a lower flow stress, higher age-hardening response and smaller quenching sensitivity.