Analytical Modeling Of Residual Stress Research Articles

Analytical model of residual stress in ultrasonic rolling of 7075 aluminum alloy

Ultrasonic rolling produces large values of residual compressive stress (RCS) in the surface layer of metal part, thereby significantly enhancing the fatigue resistance of the part. Ultrasonic rolling is a complex elastic-plastic deformation process, and it is difficult to accurately predict the residual stress produced by ultrasonic rolling. 7075 aluminum alloy was processed in this work. The elastic-plastic deformation caused by “loading-unloading” during ultrasonic rolling was analyzed based on Hertzian theory and elastic-plastic deformation theory. The residual stress model of ultrasonic rolling was developed by considering the effects of initial surface residual stress and plastic indentation depth. Finally, the model was verified by experiments. The numerical analysis results show that the surface RCS, the value and depth of the maximum RCS and thickness of the RCS layer increase to different degrees with the increment of the static load, the amplitude and the roller radius. The trend of the experimentally obtained surface RCS value with static load is consistent with that of the numerical calculations. The surface RCS increase with the increasing of the static load. The maximum error between the calculated RCS and the experimental result is no more than 10 %. The proposed residual stress model in ultrasonic rolling is relatively reliable.

Corrigendum for: Analytical modeling of residual stress in end-milling with minimum quantity lubrication

Corrigendum for: Analytical modeling of residual stress in end-milling with minimum quantity lubrication

Analytical modeling of residual stress in end-milling with minimum quantity lubrication

Milling with minimum quantity lubrication (MQL) is now a commonly used machining technique in industry. This paper proposed an analytical model for residual stress prediction in milling with MQL based on chip formation orthogonal cutting model and boundary lubrication effect. The effect of lubrication is considered to the change of friction coefficients and the heat loss at the flank surface, which would further affect the prediction of the cutting force and temperature. The proposed model is validated with experimental data done to AZ61A magnesium alloy and obtained a reasonable validation result. The predictive results show at the case investigated, neither feed per tooth nor depth of cut has a significant influence to the general trend of residual stress, where at the surface the residual stress is highly tensile and come to compressive at deeper depth. However, the application of MQL is shown to be able to significantly reduce the average magnitude of the residual stress.

Analytical Modeling of Residual Stress in Laser Powder Bed Fusion Considering Volume Conservation in Plastic Deformation

Residual stress (RS) is the most challenging problem in metal additive manufacturing (AM) since the build-up of high tensile RS may influence the fatigue life, corrosion resistance, crack initiation, and failure of the additively manufactured components. While tensile RS is inherent in all the AM processes, fast and accurate prediction of the stress state within the part is extremely valuable and results in optimization of the process parameters to achieve a desired RS and control of the build process. This paper proposes a physics-based analytical model to rapidly and accurately predict the RS within the additively manufactured part. In this model, a transient moving point heat source (HS) is utilized to determine the temperature field. Due to the high temperature gradient within the proximity of the melt pool area, the material experiences high thermal stress. Thermal stress is calculated by combining three sources of stresses known as stresses due to the body forces, normal tension, and hydrostatic stress in a homogeneous semi-infinite medium. The thermal stress determines the RS state within the part. Consequently, by taking the thermal stress history as an input, both the in-plane and out of plane RS distributions are found from the incremental plasticity and kinematic hardening behavior of the metal by considering volume conservation in plastic deformation in coupling with the equilibrium and compatibility conditions. In this modeling, material properties are temperature-sensitive since the steep temperature gradient varies the properties significantly. Moreover, the energy needed for the solid-state phase transition is reflected by modifying the specific heat employing the latent heat of fusion. Furthermore, the multi-layer and multi-scan aspects of metal AM are considered by including the temperature history from previous layers and scans. Results from the analytical RS model presented excellent agreement with XRD measurements employed to determine the RS in the Ti-6Al-4V specimens.

Analytical Modeling of Residual Stress in Laser Powder Bed Fusion Considering Part’s Boundary Condition

Rapid and accurate prediction of residual stress in metal additive manufacturing processes is of great importance to guarantee the quality of the fabricated part to be used in a mission-critical application in the aerospace, automotive, and medical industries. Experimentations and numerical modeling of residual stress however are valuable but expensive and time-consuming. Thus, a fully coupled thermomechanical analytical model is proposed to predict residual stress of the additively manufactured parts rapidly and accurately. A moving point heat source approach is used to predict the temperature field by considering the effects of scan strategies, heat loss at part’s boundaries, and energy needed for solid-state phase transformation. Due to the high-temperature gradient in this process, the part experiences a high amount of thermal stress which may exceed the yield strength of the material. The thermal stress is obtained using Green’s function of stresses due to the point body load. The Johnson–Cook flow stress model is used to predict the yield surface of the part under repeated heating and cooling. As a result of the cyclic heating and cooling and the fact that the material is yielded, the residual stress build-up is precited using incremental plasticity and kinematic hardening behavior of the metal according to the property of volume invariance in plastic deformation in coupling with the equilibrium and compatibility conditions. Experimental measurement of residual stress was conducted using X-ray diffraction on the fabricated IN718 built via laser powder bed fusion to validate the proposed model.

Analytical modeling of residual stress in direct metal deposition considering scan strategy

Existence of high tensile residual stress in the additively manufactured parts result in part failure due to crack initiation and propagation. Herein, a physics-based analytical model is proposed to predict the stress distribution much faster than experimentation and numerical methods. A moving point heat source approach is used to predict the in-process temperature field within the build part. Thermal stresses induced by steep temperature gradient is determined using the Green’s functions of stresses due to the point body load in a homogeneous semi-infinite medium. Then, both the in-plane and out of plane residual stress distributions are found from incremental plasticity and kinematic hardening behavior of the metal, in coupling with the equilibrium and compatibility conditions. Due to the steep temperature gradient in this process, material properties vary significantly. Hence, material properties are considered temperature dependent. Moreover, the specific heat is modified to include the latent heat of fusion required for the phase change. Furthermore, the multi-layer and multi-scan aspects of the direct metal deposition process are considered by incorporating the temperature history from the layers and scans. Results from the analytical residual stress model showed good agreement with X-ray diffraction measurements, which is used to determine the residual stresses in the IN718 specimens.

Residual stresses and strains analysis in press-braking bending parts considering multi-step forming effect

Press-braking bending is a multi-step bending process and widely applied in the aerospace industry. Residual stresses and strains generated during the forming process play an important role in determining its forming parameters and bending path. This work aims to analyze the residual stresses and strains in press-braking bending parts using both the theoretical method and numerical method. First, the analytical model of residual stress and strain is established based on the elastic–plastic bending theory. Second, a fully finite element model of press-braking bending has been developed, and a procedure to simulate the multi-step bending process is presented by using the elastic–plastic large deformation finite element method. The simulation results are then compared with three-point bending experiments in terms of forming force and final shapes of the bent specimens, and excellent agreement is achieved. Finally, the results calculated from the analytical model are compared with the numerical results. The distributions of residual stresses and strains on the finished plate along the length and thickness direction, and particularly the multi-step forming effect on residual stresses and strains, are discussed. It is found that the residual stresses and strains decrease at the initial loading position along the thickness direction during the forming process of subsequent loading positions. With the same punch displacement, the residual stresses and strains at the initial loading position are less than those at the subsequent bending position.

An analytical model of residual stress in orthogonal cutting based on the radial return method

Residual stress in metal cutting is critical due to its direct influence on the performance of components. An analytical model of residual stress in orthogonal cutting is established in this paper. A constitutive stress updating algorithm based on the radial return (R-R) method is firstly employed in the plastic stress calculation of the residual stress analytical model. A thermal-mechanical model for the elastic stress in orthogonal cutting is established. Subsequently, the plastic stress is calculated based on the R-R method. The R-R method and corresponding stress release method are employed to model the residual stress on the machined surface. Orthogonal cutting experiments and residual stress measurements are conducted to verify the theoretical model proposed in this work. The consistency between the prediction values and the experiment results demonstrates the accuracy of the prediction model developed in this work. According to the theoretical model, the variations in the stress components, equivalent stress and yield stress during the stress updating process are analyzed. Comparisons for the discrepancy of the accuracy between the R-R method and the present plastic stress updating methods are carried out. The characteristics and advantages of the R-R method are discussed in detail to explain the reasons for the discrepancy in the accuracy compared with current methods. The results show that the analytical model proposed in this work can achieve a better prediction accuracy than the existing models, since the R-R method can avoid the problems of stress mutation and yield drift, and exhibits excellent flexibility and extensibility by reasonable assumptions and implicit calculation method.

Optimization of residual stress field in ultrasonic assisted burnishing process

Surface compressive residual stress and its penetration depth are of important characteristics of burnishing process. The higher values compressive residual stress in the surface of the treated sample can delay the fatigue crack initiation; also, the further penetration depth restricts fatigue crack propagation. However, achieving both of performance at same time needs careful selection of burnishing parameter. In the present study an optimization approach is made to maximize the value of surface compressive residual stress subjected to specified penetration depth. The analytical model of residual stress previously developed by the author is firstly modified with a cubic interval function and then used to find how the ultrasonic assisted burnishing factors i.e. static force, vibration amplitude, ball diameter and material influence the residual stress field distribution. Then the model was then incorporated with particle swarm optimization algorithm to find optimal parameter setting. Results showed that it isn't possible to maximize both the surface compressive residual stress and its penetration depth at same time. Furthermore, to have maximum value of compressive residual stress magnitude at the surface with the penetration depth of 0.5 mm, it is required to use tungsten carbide ball with 3 mm diameter; also, the static load and vibration amplitude should be selected at the values of 120 N and 14 μm. The compressive surface residual stress in optimized condition is about 110 MPa that is compatible well with the 98 MPa obtained by confirmatory experiment. Also, the maximum depth compressive residual stress for optimum condition measured by experiment is 0.7 mm while it is predicted 0.8 mm by analytical approach.

Analytical modeling of residual stress in orthogonal cutting considering tool edge radius effect

Machining-induced residual stress is a leading cause of machining distortion. Many previous studies have been performed to model the relationship between various impact factors and machined residual stress, such as cutting parameters, lubrication, and cooling conditions etc. While few analytic studies examining the size effect of tool edge radius on residual stress have been performed. In order to better understanding the size effect of tool edge radius on machining-induced residual stress, thermomechanical coupling loading and unloading operations are applied to obtain the machining-induced residual stress on the basis of modeling mechanical loads and thermal loads for cutting with edge radiused cutters. Verification experimental results indicate that the proposed model is effective in judging and analyzing the characteristics of the residual stress profile beneath the machined surface in consideration of the tool edge radius effect. By case studies of Ti-6Al-4V turning those based on the proposed model, it was found that the value of surface residual stress increased with the tool edge radius changed from 0.01 mm to 0.03 mm, and the increased percentage of stresses in cutting and cutting width directions could be 132.6% and 191.1%, respectively. While the peak value of the compressive stress and the depth of the peak value decreased gradually, and the decreased percentages of the peak value of the compressive stress in cutting and cutting width directions are 77.8% and 88.6%. The decreased percentages of the depth of the peak value in cutting and cutting width directions are 47.6% and 63.5%.

Correction to: Analytical modeling of residual stress in helical end milling of nickel-aluminum bronze

The affiliation of the original version of this article contained a mistake. The correct affiliation is shown below.

Analytical analysis of the mechanism of effects of machining parameter and tool parameter on residual stress based on multivariable decoupling method

Generation of machining residual stress is affected by various variables, such as workpiece material, machining parameter and tool parameter. In this paper, these variables are decoupled into fundamental variables, including thermal conductivity, cutting force, friction coefficient on tool flank, shear angle, width of cut, length of tool flank wear, uncut chip thickness, rake angle and cutting speed. In order to reveal the mechanism of effects of machining parameter and tool parameter on residual stress, firstly, analytical model of residual stress was used to investigate independent effect of each fundamental variable on residual stress, to obtain the tendency of residual stress variation along with each fundamental variable; secondly, tendencies of residual stress variation along with different fundamental variables were compared, in order to reveal dominant physical approach of fundamental variables to affect residual stress; finally, physical mechanism of fundamental variables on residual stress were used to explain those of machining parameter and tool parameter on residual stress. The analysis results show that: (1) depth of highest compressive residual stress increases with the increase of feed rate, and decreases with the increase of cutting speed, this is because heating time increases with the increase of feed rate, and decreases with the increase of cutting speed; (2) more tensile residual stresses in machined surface layer generates along with the increase of tool flank wear, this is caused by the increase of length of tool flank wear and friction coefficient on tool flank; (3) residual stress amplitude increases with the increase of rake angle, this is because cutting force increase with the decrease of rake angle; also, depth of highest compressive residual stress increase with the decrease of rake angle, this is because shear angle decrease with the decrease of rake angle which further cause the increase of heating time.

An Enhanced Analytical Model of Residual Stress for Peripheral Milling

Efficient prediction of the residual stress of peripheral milling is a critical issue in academic research and industrial practice. An enhanced analytical method is developed based on inclusion theory, taking account of the sequential effect of varying thermal-mechanical load due to periodic instantaneous chip thickness. Provided with accurate analysis of the deformation in metal cutting, rigorous solution is available in principle for arbitrary two-dimensional residual stress field in complex cutting process, which is difficult to tackle by traditional relaxation procedure. Combined with mechanistic model of cutting force and approximate incremental analysis of inelastic contact, two-dimensional residual stress profile in peripheral milling is achieved efficiently by the proposed method for the first time. The predictions are verified experimentally by the X-ray diffraction measurements on the flat specimens of AISI4340 steel.

Analytical modeling of residual stress in helical end milling of nickel-aluminum bronze

The end milling of nickel-aluminum alloy has been widely applied to the manufacture of seawater applications, while the prediction of residual stress induced by this process is seldom reported. An analytical model of residual stress is proposed, based on mechanical loading and thermal loading during end milling. For the first time, the sequential discontinuous variable mechanical loading feature of end milling is taken into consideration. Also, the analytical model of stress field in the workpiece during cutting is analyzed which is intermediate variable to study residual stress. Model predictions are compared with experimental data and FEM method for cutting forces, cutting temperature, and residual stress.

An Analytical Model of Residual Stress for Flank Milling of Ti-6Al-4V

Residual stress is one of the most critical parameters in surface integrity, which has a great impact on fatigue life of the machined components. While the flank milling of titanium alloy Ti-6Al-4V has been widely applied to the manufacture of jet engine for its high productivity in aerospace industry, prediction of residual stress induced by this process is seldom reported. In this paper, an analytical model of residual stress is proposed, based on comprehensive analysis of the mechanical loading during flank milling. For the first time, the sequential discontinuous variable loading feature of flank milling is taken into consideration. An incremental elasto-plastic method followed by a relaxation procedure is used to get the stress-strain history of an arbitrary point in the subsurface so as to predict the residual stress retained in the workpiece after several loading cycles. We find that during the last phase in which the machined surface is generated, the main load comes from the plough effect of cutting edge as the uncut depth approaches zero. The simulation results indicate that the flank milled surface shows more compressive residual stress in the axial direction than in the feed direction. To validate the prediction, a series of cutting tests are conducted on Ti-6Al-4V using finish parameters and X-ray diffraction is utilized to obtain the residual stress.

Improved analytical model for residual stress prediction in orthogonal cutting

The analytical model of residual stress in orthogonal cutting proposed by Jiann is an important tool for residual stress prediction in orthogonal cutting. In application of the model, a problem of low precision of the surface residual stress prediction is found. By theoretical analysis, several shortages of Jiann’s model are picked out, including: inappropriate boundary conditions, unreasonable calculation method of thermal stress, ignorance of stress constraint and cyclic loading algorithm. These shortages may directly lead to the low precision of the surface residual stress prediction. To eliminate these shortages and make the prediction more accurate, an improved model is proposed. In this model, a new contact boundary condition between tool and workpiece is used to make it in accord with the real cutting process; an improved calculation method of thermal stress is adopted; a stress constraint is added according to the volume-constancy of plastic deformation; and the accumulative effect of the stresses during cyclic loading is considered. At last, an experiment for measuring residual stress in cutting AISI 1045 steel is conducted. Also, Jiann’s model and the improved model are simulated under the same conditions with cutting experiment. The comparisons show that the surface residual stresses predicted by the improved model is closer to the experimental results than the results predicted by Jiann’s model.

Analytical modeling of residual stress and the induced deflection of a milled thin plate

Predictions of residual stress-induced deformations on thin aerospace parts are still among the most challenging and relevant problems in engineering applications. In this paper, a new methodology based on analytical modeling of machining mechanics is introduced in order to predict thin plate deflection induced by residual stresses given material attributes, process configurations, and parameters. The model uses an elasto-plastic constitutive behavior algorithm to predict the plastic stress, strain, and thus residual stresses. A relaxation procedure is applied upon residual stresses in order to quantify the elastic deflection when the plate is unloaded from cutting forces. Experimental validations are presented on multi-pass milling of aerospace grade aluminum alloy Al7050-T7451. The newly developed analytical model shows promise to predict the residual stresses and the thin plate deflection profile under various cutting conditions.

An improved algorithm for McDowell’s analytical model of residual stress

The analytical model for two-dimensional elastoplastic rolling/sliding contact proposed by McDowell is an important tool for predicting residual stress in rolling/sliding processes. In application of the model, a problem of low predicting precision near the surface layer of the component is found. According to the volumeconstancy of plastic deformation, an improved algorithm for McDowell’s model is proposed in order to improve its predicting accuracy of the surface residual stress. In the algorithm, a relationship between three normal stresses perpendicular to each other at any point within the component is derived, and the relationship is applied to McDowell’s model. Meanwhile, an unnecessary hypothesis proposed by McDowell can be eliminated to make the model more reasonable. The simulation results show that the surface residual stress predicted by modified method is much closer to the FEM results than the results predicted by McDowell’s model under the same simulation conditions.