Equivalent Temperature Field Research Articles

Thermal error analytical modeling of gear grinding machine full-closed-loop feed system based on equivalent temperature field

Thermal errors affect the machining quality to a great extent. The basis for error compensation and thermal structure optimization is thermal error modeling. However, existing analytical models encounter challenges in dealing with complex structures, determining boundary conditions and solving the temperature and deformation fields. In this paper, a thermal error analytical model of full-closed-loop feed systems based on equivalent temperature fields (ETF) is established. Firstly, the structural simplification and thermal parameter equivalence method is proposed. The machine components are equivalent to equivalent solid cuboid (ESC) with anisotropy so that the actual complex unsolvable problems are transformed into three-dimensional analytically solvable problems. Considering the ambient temperature variation and other nonhomogeneous influences, the transient ETF model is obtained based on Green’s function method. Secondly, the complex structure problems are separated into simple solvable one-dimensional problems. The functional relationship between measurable temperature and key thermal parameters is established. And the optimal key thermal parameters are solved inversely. Thirdly, the equivalent thermal deformation fields (ETDFs) are calculated by the Rayleigh-Ritz method combined with the obtained ETFs and subsequently corrected with the Gamma Distribution. The thermal positioning error model of the full-closed-loop feed system is established by combining the ETDF of each component with the gear grinding machine structure. Finally, the experiments and simulations are carried out to verify the proposed method. The results show that the proposed method can accurately describe the temperature field, deformation field, and thermal error of machine tools. Compared with the classical data-driven method, it is superior in prediction accuracy and robustness.

High-speed machining simulation of Ti6Al4V using a thermo-mechanical coupling model and velocity-dependent friction model

PurposeThis study aims to establish a thermally coupled two-dimensional orthogonal cutting model to further improve the modeling process for systematic evaluation of material damage, stiffness degradation, equivalent plastic strain and other material properties, along with cutting temperature distribution and cutting forces. This enhances modeling efficiency and accuracy.Design/methodology/approachA two-dimensional orthogonal cutting thermo-mechanical coupled finite element model is established in this study. The tanh material constitutive model is used to simulate the mechanical properties of the material. Velocity-dependent friction model between the workpiece and the tool is considered. Material characteristics such as material damage, stiffness degradation, equivalent plastic strain and temperature field during cutting are evaluated through computation. Contact pressure and shear stress on the tool surface are extracted for friction analysis.FindingsSpeed-dependent friction models predict cutting force errors as low as 8.6%. The prediction errors of various friction models increase with increasing cutting forces and depths of cut, and simulation results tend to be higher than experimental data.Social implicationsThe current research results provide insights into understanding and controlling tool-chip friction in metal cutting, offering practical recommendations for friction modeling and machining simulation work.Originality/valueThe originality of this research is guaranteed, as it has not been previously published in any journal or publication.Peer reviewThe peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-05-2024-0162/

Equivalent thin-layer temperature field model (ETTM) for bolted rotors to describe interface temperature jump

Improving the accuracy and efficiency of predicting the temperature field is a crucial requirement for iteratively calculating and online monitoring the temperature field, particularly for combined structures. The heat flow movement is impeded by incomplete interface contact, resulting in a temperature jump. To address this, the equivalent thin-layer temperature field model (ETTM) is proposed to replace the interface thermal contact conductance (TCC) model. Firstly, the fractal TCC model of a bolt connection is derived based on fractal geometry. Subsequently, the contact surface of the circumferential bolt connection is considered to be the parallel connection of multiple bolt thermal resistances. The TCC of the equivalent thin-layer is obtained. Building on this, the ETTM of the built-up rotor structure is developed. Finally, a temperature field model of the bolted rotor is derived. The validity of models is verified by comparing the model proposed in this paper with the previous research findings and ANSYS analysis results. Numerical simulation results reveal that TCC is influenced by several factors: contact pressure, the nominal contact area within the fractal domain, fractal dimension, fractal roughness, and the root mean square (RMS) height. Furthermore, the effects of the thickness of the thin layer model and the thermal conductivity of the material on heat transfer are examined. Ultimately, the findings indicate that heat transfer at the interface is significantly impeded by thermal contact resistance across various temperature boundary conditions. Notably, lower contact pressure intensifies this impedance.

Mechanisms Underlying the Overturning Failure of Terraced Field Side Walls Due to Expansive Soil Swelling During Layer‐By‐Layer Saturation

The stability of side walls in terraced fields constructed within expansive soil regions represents a critical challenge, often leading to structural failure due to the unique wetting–swelling behavior of the soil. This study employs a comprehensive approach, integrating analytical and numerical methods to elucidate the mechanism of overturning failure attributed to the swelling effect of expansive soil under conditions of layer‐by‐layer saturation. Initially, the earth pressure acting on side walls, constructed from fiber ecological bags, is assessed in their natural, unsaturated state using Bishop’s formula for unsaturated shear strength. The study further explores the failure mode through one‐dimensional analytical analysis, focusing on the horizontal and unrestrained expansion of expansive soil during progressive saturation. Subsequently, the deformation of the side wall and the swelling effect of the soil are numerically evaluated. This is achieved by analogizing the wetting–swelling deformation field in expansive soil to an equivalent temperature field, thereby facilitating the use of finite element numerical simulation to investigate the overturning failure mechanism. Findings indicate that in the natural unsaturated state, the side walls remain stable under no earth pressure. However, as saturation depth attains a critical depth of 1.4 m during layer‐by‐layer saturation, the upper wall rotates outward in the form of local overturning failure, and the corresponding infiltration saturation depth is the critical depth for the local instability of the side wall. The investigation identifies the wetting–swelling effect as the predominant factor leading to the structural failure of side walls in terraced fields situated in expansive soil areas. Moreover, a critical infiltration saturation depth of 2.6 m is determined, beyond which the stability of the side walls is compromised. This research contributes significantly to the understanding of the failure mechanisms affecting terraced agricultural infrastructures in expansive soil regions, offering a theoretical foundation for the development of more resilient construction strategies.

Effects of EGR on combustion and emission characteristics of PODE/methanol RCCI mode at high load

In order to extend the high-load operation range of polyoxymethylene dimethyl ethers (PODE)/methanol dual-fuel reactivity controlled compression ignition (RCCI) combustion mode, a numerical model of in-cylinder combustion was established by coupling PODE/methanol chemical reaction kinetics with CONVERGE software. And then the influence mechanism of exhaust gas recirculation (EGR) addition on in-cylinder combustion process, combustion stability and pollutant formation of the RCCI engine under high load and pilot injection strategy were investigated. The results show that with the increase of EGR ratio, the peak values of the first heat release formed by PODE pilot injection combustion and in-cylinder pressure decrease, the combustion start timing and CA50 phase are gradually delayed. While the peak value of the second heat release formed by PODE main injection combustion at low EGR ratio and the combustion duration remain unchanged. Meanwhile, as the EGR ratio increases from 0 to 30 %, the brake thermal efficiency (BTE) decreases from 46.54 % to 44.40 %. And the in-cylinder equivalent ratio and temperature field distributions become uniform, and both high-temperature region (above 1800 K) and NOx generation area are reduced, which decreases NOx emissions by 42.6 % without increasing soot emissions. The methanol mixture at squish zone is subjected to the high-temperature and high-pressure of pilot injection combustion, resulting in obvious pressure oscillation. While EGR addition decreases the generation of HCO and OH active radicals, ignition points and reaction rate, which effectively inhibits methanol spontaneous combustion and knock phenomenon, and decreases the ringing intensity from 2.82 MW/m2 to 1.50 MW/m2. The pilot injection strategy coupled with 18 % EGR can extend the indicated mean effective pressure to 1.22 MPa. However, the load further extension is mainly limited by the sharp decline of BTE.

Influence of temperature and plastic deformation on AA2024 T3 friction stir welded joint microstructure

This paper deals with analysis and comparison of the equivalent plastic strain and temperature fields in the aluminium alloy 2024 T3 (AA2024 T3) joint, with macro/microstructure appearance and hardness profile. In the alloys hardened by heat treatment, grain size and particle size of the precipitate are functions of equivalent plastic strain, strain rate and temperature. By analysing the equivalent plastic strain fields and temperature fields it is possible, to some extent, to capture the effect of welding parameters and thermo-mechanical conditions on grain structure, and therefore hardness and strength in the welded joint. A coupled thermo-mechanical model is applied to study the material behaviour during the linear welding stage of friction stir welding. The 3-D finite element model has been created in ABAQUS/EXPLICIT software using the Johnson-Cook material law. The values of thermo-mechanical quantities during the welding stage are obtained from the numerical model and shown as distributions across the joint. The obtained values of these quantities are related to the microstructure of the joint zones and hardness distribution, and this relation is discussed.

The Use of an Equivalent Temperature Field to Emulate an Induced Residual Stress Field in a Rotating Disk Due to Full Or Partial Rotational Autofrettage

Abstract The evaluation of equivalent temperature fields for cylindrical and spherical pressure vessels to imitate autofrettage induced residual stresses has been successfully implemented in studying crack growth in autofrettaged vessels by the finite element method. Rotational autofrettage is a recent method that can be employed for strengthening hollow disks used in many turbomachinery. The evaluation of the equivalent temperature field becomes pivotal in the performance assessment of autofrettaged cracked disks subjected to high rotational speed. In this work, an equivalent thermal loading method for emulating the residual stress field in a hollow rotating disk, induced by full or partial rotational autofrettage in a finite element analysis is suggested. An analytical, or a numerical discrete solution, evaluating the equivalent temperature field for an arbitrary axisymmetric residual stress field, induced in a rotating disk due to rotational autofrettage, is developed. This solution is implemented in a finite element analysis to emulate the original rotational autofrettage induced residual stresses in a typical rotating disk. Applying the equivalent temperature field, the residual stresses obtained in the finite element analysis, are further corroborated with the original residual stress field introduced by rotational autofrettage. It is found that the developed equivalent temperature fields excellently reproduce the residual stress fields, within less than 1%, induced by both full or partial rotational autofrettage.

Impact of Assimilating High‐Resolution Atmospheric Motion Vectors on Convective Scale Short‐Term Forecasts: 2. Assimilation Experiments of GOES‐16 Satellite Derived Winds

AbstractBuilding on the results from the observing system simulation experiments in Part I, this study investigates the impact of assimilating Geostationary Operational Environmental Satellite‐16 (GOES‐16) derived atmospheric motion vector (AMV) data on the convective scale numerical weather prediction (NWP) by using the National Severe Storms Laboratory (NSSL) three‐dimensional variational (3DVAR) data assimilation (DA) system. The benefit of the AMV DA for short‐term severe weather forecast is assessed with three high‐impact weather events that occurred in spring 2018 and 2019 over the Great Plains of the United States. The results show that the wind and equivalent potential temperature fields associated with the storm environment and the nearby ongoing convection are improved by the AMV DA, which yields better simulation of the boundaries and the subsequent forecasts of storm evolution. For the quasi‐linear or mesoscale convective system, the assimilation of AMVs has a positive impact on the 0–3 h forecasts of composite reflectivity and accumulated precipitation in terms of the shape, location, and magnitude. However, the AMV DA has difficulty in capturing the sharp moisture gradient associated with the dryline and mostly underpredicts the associated scattered storms.

Dynamic thermal camouflage via a liquid-crystal-based radiative metasurface

Abstract Thermal camouflage, which is used to conceal objects in the infrared vision for confrontation with infrared detection in civilian or military applications, has garnered increasing attraction and interest recently. Compared with conductive thermal camouflage, that is to tune heat conduction to achieve equivalent temperature fields, radiative thermal camouflage, based on emissivity engineering, is more promising and shows much superiority in the pursuit of dynamic camouflage technology when resorting to stimuli-responsive materials. In this paper, we demonstrate the emissivity-engineered radiative metasurface to realize dynamic thermal camouflage functionality via a flying laser heat source on the metal-liquid-crystal-metal (MLCM) platform. We employ a rigorous coupled-wave algorithm to calculate the surface emissivity of Au/LC/Au microstructures, where the LC-orientation angle distribution is quantified by minimizing the emitted thermal energy standard deviation throughout the whole plate. Emissivity engineering on the MCLM platform is attributed to multiple magnetic polariton resonance, and agrees well with the equivalent electric circuit analysis. Through this electrical modulation strategy, the moving hot spot in the original temperature field is erased and a uniform temperature field is observed in the infrared camera instead, demonstrating the very good dynamic thermal camouflage functionality. The present MLCM-based radiative metasurface may open avenues for high-resolution emissivity engineering to realize novel thermal functionality and develop new applications for thermal metamaterials and meta-devices.

Prediction of landfalling Bay of Bengal cyclones during 2013 using the high resolution Weather Research and Forecasting model

AbstractThe present study investigated the capability of the Weather Research and Forecasting (WRF) model in the forecast/simulation of five landfalling Bay of Bengal (BoB) cyclones during 2013. A 3D variational (3DVar) method of data assimilation of the WRF model was used to assimilate the Global Telecommunication System and satellite radiances to improve the initial conditions. The results demonstrated that the model has the ability to simulate the cyclone track, intensity and structure. The study also indicates that predicted storm track, landfall and intensity improved with the 3DVar technique compared to without it. This was due to better initial conditions in the 3DVar experiment. The predicted track errors of the five storms were compared to available global and regional forecasting systems and the results show that the model has the capability for prediction of cyclones over the BoB region. The forecasted mean track errors were about 70, 114, 182 and 184 km; minimum centre pressure was about 8, 10, 13, 13 hPa and maximum surface wind was about 6, 10, 9, 8 m·s−1 on day 1 to day 4 forecast respectively. The study also presents some of the important predicted diagnostic parameters such as temperature anomaly, divergence, heating rate, frozen hydrometeors, vorticity field, equivalent potential temperature, maximum reflectivity, accumulated rainfall and horizontal wind fields compared to available observations for the extremely severe cyclonic storm Phailin. The warm core structure of the Phailin cyclone was resolved in the model between 9 and 15 km compared to satellite observations. The statistical analysis, distribution and magnitude of forecasted accumulated rainfall are also compared to the rainfall of 174 automatic weather stations.

Comparative Study on Constitutive Models for 21-4N Heat Resistant Steel during High Temperature Deformation.

The Gleeble-1500D thermal simulation test machine was used to conduct the isothermal compression test on 21-4N at the strain rate () of 0.01–10 s−1, the deformation temperature (T) of 1273–1453 K and the maximum deformation is 0.916. The data of the stress-strain (σ-ε) were obtained. Based on the σ-ε data, the Johnson-Cook (J-C), modified J-C, Arrhenius and Back-Propagation Artificial Neural Network (BP-ANN) models were established. The accuracy of four models were verified, analyzed and compared. The results show that J-C model has a higher accuracy only under reference deformation conditions. When the deformation condition changes greatly, the accuracy of J-C model is significantly reduced. The coupling effect of T and of modified J-C model is considered, and the prediction accuracy is greatly improved The Arrhenius model introduces Zener-Hollomon (Z) to represent the coupling effect of T and , it has a fairly high prediction accuracy. And it can predict flow stress (σ) accurately at different conditions. The accuracy of BP-ANN model is the highest, but its learning rate is low, the learning and memory are unstable. It has no memory for the weights and thresholds of the completed training. So, there are certain limitations of it in use. Finally, a Finite Element Method (FEM) of the isothermal compression experiment for four models were established, and the distribution of the equivalent stress field, equivalent strain field and temperature field with the deformation degree of 60% were obtained.

Development of efficient distortion prediction numerical method for laser additive manufactured parts

Part distortion is a technical bottleneck in the field of laser solid forming additive manufacturing (AM). Finite element modeling has shown great power in analyzing and predicting thermal distortion during laser AM process. However, as the global size of the manufactured component increases, the conventional numerical method appears limited due to the long computation time. In this paper, the temperature distribution and the evolution of a Ti-6Al-4V thin wall during the AM process were investigated first via the transient heat transfer analysis. “Quasi-steady state” characteristic of the temperature distribution was observed after depositing several layers. Based on this, an efficient equivalent temperature field (ETF) method was developed to predict thermal distortion by extracting the quasi-steady temperature field and applying it as a thermal boundary during mechanical analysis. The developed ETF method was validated by the good agreement in the predicted distortion distribution pattern and magnitude compared with that predicted by the conventional move heat source numerical method. The developed ETF method in this paper significantly saved computation time by above 90% during mechanical analysis. Furthermore, the distortion of laser additive manufactured thin wall with 266 layers was successfully predicted by the ETF method within several hours. The maximum deviation is 29.3% compared with the experimental results. The proposed method provides the possibility to predict distortion for large-scale AM parts, which may have the potential application in engineering.

The cumulative detrimental impact of pressure and autofrettage on the fatigue life of an externally cracked modern tank gun barrel

The fatigue life of an externally cracked modern tank gun barrel is controlled by the prevailing combined stress intensity factor (SIF) <em>K</em>_<em>IN</em>, which consists of two components:<em>K</em>_<em>IP</em>-the SIF caused by internal pressure; <em>K</em>_<em>IA</em>-the positive SIF due to the tensile residual stresses induced by autofrettage. <em>K_IA</em> values for a single external radial semi-elliptical crack originating at the outer surface of an autofrettaged gun barrel were calculated for a large number of crack configurations by Perl and Saley. In order to assess the combined effect of overstraining and the pressurizing of the barrel during firing, values of <em>K</em>_<em>IP</em>, the SIF caused by internal pressure, and those of <em>K</em>_<em>IN</em>, the combined SIF, are evaluated. The 3D analysis is performed using the finite element method (FEM) employing singular elements along the crack front. The novel realistic overstrain residual stress fields, incorporating the Bauschinger effect, for the three types of autofrettage, Swage, Hydraulic and Hill's, previously developed, are applied to the barrel. The RSFs are simulated in the finit element (FE) analysis using equivalent temperature fields. Values of <em>K</em>_<em>IP</em> and <em>K</em>_<em>IN</em> are evaluated for a typical barrel of radii ratio <em>R</em>_<em>0</em>/<em>R</em>_<em>i</em>=2, crack depths (<em>a/t</em>=0.005-0.1), crack ellipticities (<em>a/c</em>=0.2-1.0), and five levels of the three types of autofrettage, (<em>ε</em>=40%, 60%, 70%, 80%, and 100%). A detailed analysis of the effect of the above parameters on the prevailing SIF is conducted. All three types of autofrettage are found to have a detrimental effect on the barrel's fatigue life. However, the magnitude of life reduction is autofrettage-type dependent. In the case of external cracking, Hydraulic autofrettage is found to be somewhat superior to Swage autofrettage, and Hill's autofrettage is found to be non-realistic. Finally, the results accentuate the importance of the three dimensional analysis and the incorporation of the Bauschinger effect.

Azimuthally averaged structure of Hurricane Edouard (2014) just after peak intensity

Analyses of dropsonde data collected in Hurricane Edouard (2014) just after its mature stage are presented. These data have unprecedentedly high spatial resolution, based on 87 dropsondes released by the unmanned NASA Global Hawk from an altitude of 18 km during the Hurricane and Severe Storm Sentinel (HS3) field campaign. Attempts are made to relate the analyses of the data to theories of tropical cyclone structure and behaviour. The tangential wind and thermal fields show the classical structure of a warm‐core vortex, in this case with a secondary eyewall feature. Additionally, the equivalent potential temperature field (θe) shows the expected structure with a mid‐tropospheric minimum at outer radii and contours of θe flaring upwards and outwards at inner radii. With some imagination, these contours are roughly congruent to the surfaces of absolute angular momentum. However, details of the analysed radial velocity field are quite sensitive to the way in which the sonde data are partitioned to produce an azimuthal average. This sensitivity is compounded by an apparent limitation of the assumed steadiness of the storm over the period of data collection.

The detrimental effect of autofrettage on externally cracked modern tank gun barrels

Overstraining gun tubes has a twofold advantage. First, it enables the increase of the Safe Maximum Pressure (SMP) in the tube, resulting in a higher muzzle velocity which extends the gun's range and its projectile kinetic energy. Second, it reduces the tube's susceptibility to internal cracking which prolongs its fatigue life. Unfortunately, autofrettage also bears an inherent detrimental effect as it considerably increases the tensile hoop stress at the outer portion of the barrel's wall, which enhances external cracking of the tube by increasing the prevailing Stress Intensity Factor (SIF). In order to quantify this disadvantageous effect, 3-D Mode I SIFs distributions along the front of a single external radial semi-elliptical crack initiating from the outer surface of an autofrettaged modern gun barrel, overstrained by either the Swage or the Hydraulic autofrettage processes, are evaluated. The analysis is performed by the finite element (FE) method, using singular elements along the crack front. Innovative residual stress fields (RSFs), incorporating the Bauschinger effect for both types of autofrettage are applied to the barrel. Hill's [1] RSF is also applied to the tube for comparison reasons. All three RSFs are incorporated in the FE analysis, using equivalent temperature fields. Values for KIA - the SIF resulting from the tensile residual stresses induced by autofrettage are evaluated for: a typical barrel of radii ratio Ro/Ri = 2, crack depth to wall-thickness ratios (a/t = 0.005–0.1), crack ellipticities (a/c = 0.2–1.0), and five levels of Swage, Hydraulic and Hill's autofrettage (ε = 40%, 60%, 70%, 80%, and 100%). In total, 375 different 3-D cases are analyzed. The analysis demonstrates undoubtedly the detrimental effect of all types of autofrettage in increasing the prevailing effective stress intensity factor of external cracks, resulting in crack initiation enhancement and crack growth rate acceleration which considerably shortens the total fatigue life of the barrel. Nonetheless, the detrimental effect is autofrettage-type dependent. Swage and Hydraulic autofrettage RSFs differ substantially from each other. The disadvantageous effect of Swage autofrettage is much greater than that resulting from Hydraulic autofrettage. The results also emphasize the significance of the Bauschinger effect and the importance of the 3-D analysis.

The beneficial effect of full or partial autofrettage on the combined 3-D stress intensity factors for inner coplanar crack arrays and ring cracks in a spherical pressure vessel

The distributions of the combined 3-D Stress Intensity Factor (SIF), KIN = KIP + KIA, due to both internal pressure and autofrettage along the front of coplanar crack arrays as well as ring cracks emanating from the bore of an overstrained spherical pressure vessel are evaluated. The 3-D analysis is performed using the finite element (FE) method employing singular elements along the crack front. A novel realistic autofrettage residual stress field incorporating the Bauschinger effect is applied to the vessel. The residual stress field is simulated using an equivalent temperature field in the FE analysis. Numerous coplanar crack array configurations are analyzed as well as ring cracks of various depths. SIFs distributions are evaluated for coplanar crack arrays of densities δ = 0–0.95, consisting of cracks of depth to wall thickness ratios of a/t = 0.05–0.4, and ellipticities of a/c = 0.2–1.0, prevailing in fully or partially autofrettaged spherical vessels of different geometries R0/Ri = 1.1, 1.2, and 1.7, bearing three levels of autofrettage (ε = 50%, 75%, and 100%). Furthermore, SIFs for inner ring cracks of various crack depth to wall thickness ratios of a/t = 0.025–0.6 prevailing in the same fully or partially autofrettaged spherical pressure vessels are also evaluated. In total, about two hundred different crack configurations are analyzed. A detailed study of the influence of the above parameters on the prevailing SIF is conducted. The results clearly demonstrate the favorable effect of autofrettage which may considerably reduce the prevailing effective stress intensity factor, thus delaying crack initiation and slowing down crack growth rate, and hence, substantially prolonging the total fatigue life of the vessel. Furthermore, the results emphasize the importance of properly accounting for the Bauschinger effect including re-yielding, as well as the significance of the three-dimensional analysis herein performed. Furthermore, it is shown that in some cases the commonly accepted approach that the SIF for a ring crack of any given depth is the upper bound to the maximum SIF occurring in an array of coplanar cracks of the same depth is not universal.

Structure analyses of the explosive extratropical cyclone: A case study over the Northwestern Pacific in March 2007

The synoptic situation and mesoscale structure of an explosive extratropical cyclone over the Northwestern Pacific in March 2007 are investigated through weather station observations and data reanalysis. The cyclone is located beneath the poleward side of the exit of a 200 hPa jet, which is a strong divergent region aloft. At mid-level, the cyclone lies on the downstream side of a well-developed trough, where a strong ascending motion frequently occurs. Cross-section analyses with weather station data show that the cyclone has a warm and moist core. A ‘nose’ of the cold front, which is characterized by a low-level protruding structure in the equivalent potential temperature field, forms when the cyclone moves offshore. This ‘nose’ structure is hypothesized to have been caused by the heating effect of the Kuroshio Current. Two low-level jet streams are also identified on the western and eastern sides of the cold front. The western jet conveys cold and dry air at 800–900 hPa. The wind in the northern part is northeasterly, and the wind in the southern part is northwesterly. By contrast, the eastern jet carries warm and moist air into the cyclone system, ascending northward from 900 hPa to 600–700 hPa. The southern part is dominated by the southerly wind, and the wind in the northern part is southwesterly. The eastern and western jets significantly increase the air temperature and moisture contrast in the vicinity of the cold front. This increase could play an important role in improving the rapid cyclogenesis process.

Swage and hydraulic autofrettage impact on fracture endurance and fatigue life of an internally cracked smooth gun barrel Part I – The effect of overstraining

Three dimensional Mode I Stress Intensity Factor (SIF) distributions along the front of a single inner radial semi elliptical crack emanating from the bore of an autofrettaged smooth gun barrel are evaluated. The barrel is assumed to have been overstrained by either the Swage or the Hydraulic autofrettage processes. The 3-D analysis is performed using the finite element (FE) method employing singular elements along the crack front. Novel realistic overstrain residual stress fields, incorporating the Bauschinger effect, for the two autofrettage processes are applied to the barrel. For comparison reasons Hill's (Hill, 1950) residual stress field (RSF) is also applied. The RSFs for Swage and Hydraulic autofrettage as well as Hill's solution are simulated in the FE analysis using equivalent temperature fields. Values for KIA - the SIF resulting from the compressive residual stresses induced by autofrettage are evaluated for a typical barrel of radii ratio R0/Ri=2, a wide range of crack depth to wall-thickness ratios (a/t=0.005–0.1), various crack ellipticities (a/c=0.2–1.0), and five levels of Swage, Hydraulic and Hill's autofrettage (ε=40%, 60%, 70%, 80%, and 100%). In total, 375 different 3-D crack cases are analyzed. A detailed study of the influence of the above parameters on the prevailing SIF is conducted. The results clearly indicate the favorable effect of all three types of autofrettage in reducing the prevailing effective stress intensity factor and thus delaying crack initiation, slowing down crack growth rate, and substantially prolonging the total fatigue life of the barrel. However, the favorable effect of autofrettage is type-dependent. The realistic Swage and Hydraulic autofrettage RSFs are found to differ considerably from each other. The beneficial effect of Swage autofrettage is found to be considerably superior to that resulting from Hydraulic autofrettage. Hill's autofrettage is far from being realistic as it overestimates the RSF magnitude and thus exaggerates the beneficial effect of autofrettage. Finally, the results highlight the importance of properly accounting for the Bauschinger effect including re-yielding, as well as the significance of the three dimensional analysis herein performed.

Swage and hydraulic autofrettage impact on fracture endurance and fatigue life of an internally cracked smooth gun barrel Part II – The combined effect of pressure and overstraining

The distributions of KIA (the stress intensity factor (SIF) due to autofrettage) along the front of a single inner radial semi-elliptical crack emanating from the bore of an autofrettaged smooth gun barrel were calculated for a large number of crack configurations in Part I of this paper. In order to assess the combined effect of overstraining and pressurizing the barrel, values of KIP, the SIF caused by internal pressure, and those of KIN, the combined SIF, are evaluated. The 3-D analysis is performed using the finite element (FE) method employing singular elements along the crack front. The novel realistic overstrain residual stress fields, incorporating the Bauschinger effect, for the two types of autofrettage presented in Perl and Saley (2016) are applied to the barrel. Hill's (Hill, 1950) residual stress field (RSF) is also applied for comparison reasons. The RSFs for Swage and Hydraulic autofrettage as well as Hill's solution are simulated in the FE analysis using equivalent temperature fields. Values of KIP and KIN=KIP+KIA are evaluated for a typical barrel of radii ratio R0/Ri=2, a wide range of crack depth to wall-thickness ratios (a/t=0.005–0.1), various crack ellipticities (a/c=0.2–1.0), and five levels of Swage, Hydraulic and Hill's autofrettage (ε=40%, 60%, 70%, 80%, and 100%). In total, 375 different 3-D cases are analyzed. A detailed study of the influence of the above parameters on the prevailing SIF is conducted. The results clearly indicate the favorable effect of all three types of autofrettage in enhancing the fatigue life of the barrel. However, the magnitude of such life extension depends on the type of autofrettage employed. Among the two realistic overstrain processes, Swage autofrettage is found to be considerably superior to Hydraulic autofrettage in prolonging the barrel's fatigue life. Hill's autofrettage is far from being realistic, overestimating the magnitude of the RSF, and, thus, exaggerating the barrel's fatigue life. Finally, the results highlight the importance of properly accounting for the Bauschinger effect including re-yielding, as well as the significance of the three dimensional analysis herein performed.

The beneficial effect of full or partial autofrettage on the combined 3-D stress intensity factors for inner radial crack arrays in a spherical pressure vessel

The distributions of the combined 3-D Stress Intensity Factor (SIF), KIN=KIP+KIA, due to both internal pressure and autofrettage along the front of radial crack arrays emanating from the bore of an overstrained spherical pressure vessel are evaluated. The 3-D analysis is performed using the finite element (FE) method employing singular elements along the crack front. A novel realistic autofrettage residual stress field incorporating the Bauschinger effect is applied to the vessel. The residual stress field is simulated using an equivalent temperature field in the FE analysis. Numerous radial crack array configurations are analyzed. SIF distributions are evaluated for arrays of radial cracks containing one to twenty cracks, n=1–20, of crack depth to wall thickness ratios of a/t=0.01–0.8, and ellipticities (crack depth to crack length) of a/c=0.2–1.0 prevailing in fully or partially autofrettaged spherical vessels of outer to inner radii R0/Ri=1.1, 1.2, and 1.7, bearing three levels of autofrettage (ε=50%, 75%, and 100%). In total, about two hundred different crack configurations are analyzed. A detailed study of the influence of the above parameters on the prevailing SIF is conducted. The results clearly demonstrate the favorable effect of autofrettage which may considerably reduce the prevailing effective stress intensity factor, thus delaying crack initiation and slowing down crack growth rate, and hence, substantially prolonging the total fatigue life of the vessel. Furthermore, the results emphasize the importance of properly accounting for the Bauschinger effect including re-yielding, as well as the significance of the three dimensional analysis herein performed.