Modeling Of Residual Stresses Research Articles

Prediction of residual stress in precision injection molding of plastic optical lenses based on an improved solidification layer model

Precision injection molding technology (PIM) is the primary technique used for large scale manufacture of plastic optical lenses. However, the injection molding of plastic optical lenses results in a problem of residual stress, which affects the imaging quality of the optical system. The conventional injection molding process uses an orthogonal approach for adjusting the process parameters, requiring a large number of experiments. Therefore, this article proposes an improved residual stress model for precision injection molding of plastic optical lenses based on the solidification layer theory. The residual stress of precision injection molded aspherical plastic optical lens used for imaging optical systems was analyzed through simulation and experimentation. The results demonstrate that the proposed method achieves residual stress prediction for plastic optical lenses after injection molding.

Finite element modeling of thermal residual stresses in functionally graded aluminum-matrix composites using X-ray micro-computed tomography

Metal-ceramic composites by their nature have thermal residual stresses at the micro-level, which can compromise the integrity of structural elements made from these materials. The evaluation of thermal residual stresses is therefore of continuing research interest both experimentally and by modeling. In this study, two functionally graded aluminum alloy matrix composites, AlSi12/Al2O3 and AlSi12/SiC, each consisting of three composite layers with a stepwise gradient of ceramic content (10, 20, 30 vol%), were produced by powder metallurgy. Thermal residual stresses in the AlSi12 matrix and the ceramic reinforcement of the ungraded and graded composites were measured by neutron diffraction. Based on the X-ray micro-computed tomography (micro-XCT) images of the actual microstructure, a series of finite element models were developed to simulate the thermal residual stresses in the AlSi12 matrix and the reinforcing ceramics Al2O3 and SiC. The accuracy of the numerical predictions is high for all cases considered, with a difference of less than 5 % from the neutron diffraction measurements. It is shown numerically and validated by neutron diffraction data that the average residual stresses in the graded AlSi12/Al2O3 and AlSi12/SiC composites are lower than in the corresponding ungraded composites, which may be advantageous for engineering applications.

Thermomechanical modelling of residual stresses and distortion in laser powder bed fusion: Assessment of the effect of build plate preheating on the behaviour of Inconel 718

The fabrication of complex metallic parts via laser powder bed fusion (L–PBF) is becoming more mainstream to overcome the limitations of traditional manufacturing methods. However, L–PBF induces undesirable residual stresses (RS) and possible geometric distortion of the component. This study aims to show the capabilities of build plate preheating in mitigating both defects. A thermomechanical finite element model is developed to investigate the outcomes of various preheating conditions when producing Inconel 718 samples consisting in a base and an overhanging beam restricted with support structures. Initially, the model is calibrated against the deflection result of an academic work employing a resemblant geometry. Our study is then performed. The as–built von Mises stress evolution along two paths as well as part distortion are assessed at 100, 300, and 500°C, then compared to the reference “no preheating” case results. A peak top surface RS of 803MPa was reached without preheating and reduced by 48.69% at 500°C. Along the vertical path, the mean stress value went from 897MPa at 20°C to 474MPa at 500°C. Distortion of the as–built part is essentially a non–uniform contraction of the beam along the x–direction due to progressive bending of the supports about y–axis. Once the beam is unrestricted from the substrate, it deforms as a cantilever structure. Increasing the preheating temperature decreases the maximum build direction deflection by 14.56% at 100°C, up to 76.94% at 500°C in comparison to the 4.12mm reached at 20°C. In conclusion, preheating the substrate is a very effective way to mitigate RS and distortion in L–PBF of Inconel 718. Even the relatively low 100°C showed a notable improvement in this regard.

Analytical modelling for residual stress prediction in multi-step side milling of GH4169 thin-wall parts based on deformation

GH4169 thin-walled parts are widely used in aerospace due to their high-temperature, corrosion resistance, and fatigue strength. However, they often deform from machining-induced residual stress, which is a significant unresolved manufacturing challenge. Additionally, initial residual stress from previous steps critically impacts subsequent processes. This study found that the residual stress of side milling of thin-walled parts under smaller cutting parameters is mainly caused by mechanical effects, and the influence of milling heat can be ignored. In this study, an analytical prediction model for residual stress of multi-step side milling thin-walled parts based on the deformation of thin-walled parts is proposed for the first time, which is suitable for smaller cutting parameters. Then, the proposed model is examined the mechanisms through which residual stresses develop during side milling and defined the applicability of model based on specific assumptions. To validate these assumptions, an experimental setup was devloped to simulate the movement of the heat source during milling. Subsequent two-step side milling experiments on GH4169 confirmed the accuracy of the analytical prediction model in predicting the residual stresses of multi-step side milling in thin-walled parts. It was observed that higher equivalent bending stiffness in thin-walled parts correlates with reduced machining deformation. The analytical model also provides a strategic approach to control machining deformation by managing the equivalent bending stiffness of the parts.

Modeling of Residual Stress During EDM of AISI 4340 for Marine Propulsion Application

This investigation is conducted to estimate the extent of residual stress induced in the workpiece when machined on EDM. The Residual stresses induced post machining a product can led to lower life and inadequate failures during service. AISI 4340 finds its applicability in propulsion parts of marine engine and thus chosen as the material for study. Tungsten-Copper is selected as material for tool. Response Surface Methodology (RSM) with Central Composite Design (CCD) is utilized preparing the trails using current, on-time of pulse, voltage, and duty factor as machine variables. X-Ray Diffraction (XRD) was performed to estimate the d-space lattice of machined as well as un-machined specimens. Furthermore, Scanning Electron Microscopy (SEM) was executed to analyze effect of residual stress on surface post machining. The model suggested that voltage and on duration were crucial factors for residual stress while duty factor and current were less influential. Residual stress in the machined surface results from gradual heating and cooling during machining. The developed model was predicted to be accurate through the validation test. The micro-cracks resulted from the thermal stresses developed during machining of the workpiece.

A method: multi-scale calculation life of welded beams with residual stress

To improve the accuracy of the probability of life value calculation while ensuring computational efficiency, a study was conducted on the finite element probability of life calculation method for beam-shell coupling. On the basis of the finite element heat and stress coupling model of Type I welded beam, a fatigue fracture model of residual stress and cyclic load coupling was established. The probability of life calculation of beam-shell elements was theoretically derived, and the expression of the probability of life model was unified. The probability of life of Type I welded beam was calculated, and it was compared with the model of beam assumption and the full life test result. The results show that the computational efficiency of the beam-shell coupling model is higher than that of the shell element model. In addition, the probability of life calculation result obtained by the beam-shell coupling model is highly consistent with the experimental result in statistical terms, and it has higher accuracy at low stress levels than the calculation result of the beam element, with the relative error between the median of the calculation result and the experimental result being less than 10%.

Thermoviscoelastic modelling of highly reactive thermoset resins for liquid moulding applications

This paper presents a methodology for developing thermo-mechanical properties model for highly reactive resins and its use for Resin Transfer Moulding process (RTM) modelling and prediction of residual stresses. Cure Hardening Instantaneously Linear Elastic (CHILE), and Thermoviscoelastic (TVE) models, were implemented to analyze the mechanical behaviour of the resin. Simulation of the RTM process was developed and applied to a representative curved plate geometry. An integral approach was considered where the degree of cure gradient, generated during the filling stage due to the reactivity of the resin, was implemented as initial condition of the stress-deformation process simulation. The validation process included fabricating experimental parts with the representative geometry. The degree of cure variation of highly reactive thermosets during injection caused a significant effect on the final shape of the parts. These effects were captured by the simulations, where the TVE model showed a more accurate prediction of the part distortion.

Thermo-Chemo-Mechanical Modeling of Residual Stress in Unidirectional Carbon Fiber-Reinforced Polymers during Manufacture.

The application of carbon fiber-reinforced composite materials in marine engineering is growing steadily. The mechanical properties of unbonded flexible risers using composite tensile armor wire are highly valued. However, the curing process generates a certain amount of internal residual stress. We present a detailed analysis of epoxy resin laminates to assess the impact of thermal, chemical, and mechanical effects on the curing stress and strain. An empirical model that correlates temperature and degree of cure was developed to precisely fit the elastic modulus data of the curing resin. The chemical kinetics of the epoxy resin system was characterized using differential scanning calorimetry (DSC), while the tensile relaxation modulus was determined through a dynamic mechanical analysis. The viscoelastic model was calibrated using the elastic modulus data of the cured resin combining temperature and degree of the curing (thermochemical kinetics) responses. Based on the principle of time-temperature superposition, the displacement factor and relaxation behavior of the material were also accurately captured by employing the same principle of time-temperature superposition. Utilizing the empirical model for degree of cure and modulus, we predicted micro-curing-induced strains in cured composite materials, which were then validated with experimental observations.

A physically consistent 2D residual stress model for approximating 3D effects in welding

Welding-induced residual stresses play a critical role in fitness-for-service evaluation of pressure equipment as stipulated by codes and standards, e.g., BS 7910 and API 579 RP-1/ASME FFS-1. Due to the complex residual stress evaluation process, two-dimensional (2D) residual stress modeling is most often exercised for supporting the development of the residual stress prescriptions in these FFS codes. Two major limitations exist in such a 2D modeling approach. One is the lack of heat sink effects in the third direction, resulting in a missing linkage to the actual welding linear heat input. The other is the over-simplifications of the mechanical restraint effects on the residual stress development process by imposing generalized plane-strain or axisymmetric conditions. This paper presents a physically consistent 2D residual stress model, with which actual welding linear heat input can be consistently interpreted for use in a 2D thermal model and 3D mechanical restraint effects can be approximated through a set of closed-form expressions that can be readily implemented in available finite element procedures. The effectiveness of the proposed 2D modeling procedures is then validated against a few well-documented residual stress case studies on which experimental data are available.

Predictive modelling of residual stress in turning of hard materials using radial basis function network enhanced with principal component analysis

This study proposes a hybrid machine learning (ML) model that combines a radial basis function network (RBFN) with principal component analysis (PCA) to predict residual stress (RS) in the machining process. Higher temperatures and plastic deformation can generate RS conditions in the machining of hard materials, significantly influencing the quality of machined parts, particularly their surface integrity. It is crucial to evaluate and guarantee machining conditions that ensure reliable surface integrity that yields compressive RS conditions. Incorrect parameter settings can lead to poor surface quality, resulting in tensile RS conditions that impact both the quality and lifetime of manufactured products. The methodology involved experimental machining trials for data acquisition, with conditions selected for hard material machining tests conducted using a computer numeric control (CNC) lathe under dry cutting conditions. The cutting force components were measured, and RS was evaluated using X-ray diffraction. A total of 60 trials were conducted. Data preprocessing, including normalization and removal of outliers, was executed before constructing the ML algorithm, leaving 59 valid tests for model training and testing. Separate datasets for training (70 % of the data) and testing (30 %) were randomly selected from the valid experimental tests. PCA enhanced the RBFN model’s generalization by reducing data dimensionality and providing the hidden units parameter. The eigenvectors obtained through PCA served as an efficient initial reference for RBF centroids, highlighting principal directions of variation. The PCA-RBFN model, using a multiquadric radial function, exhibited robust performance in capturing underlying patterns during training and demonstrated balanced results in the tests. In the PCA-RBFN model training stage, it exhibited a coefficient of determination (R2) of 76.66 %, a mean average error (MAE) of 72.15 MPa, and a root mean square error (RMSE) of 84.94 MPa. In the testing stage, the model showed increased metrics, indicating its ability to predict RS values accurately, with an R2 of 80.54 %, MAE of 51.25 MPa, and RMSE of 70.36 MPa. The evaluation between the training and testing stages highlighted the model’s coherence in performance, demonstrating its ability to generalize well to new data. A second comparative analysis was conducted with a conventional RBFN approach using stochastic method for centroid determination. The hybrid PCA-RBFN method exhibited lower computational effort, requiring only three iterations compared to 221,923 iterations in the conventional approach. Despite the conventional approach yielding better metrics in the training stage, it exhibited signs of overfitting, a common concern in machine learning models. The hybrid PCA-RBFN consistently outperformed it regarding generalization and fit during testing. The proposed methodology holds practical implications for the manufacturing industry, allowing the integration of a pre-trained predictive model into machine controllers or smart sensors. The hybrid PCA-RBFN’s computationally lightweight approach also supports incorporating real-time adaptive algorithms into production systems, enabling continuous real-time adjustments to the model factors and weights, thereby improving automated control.

Dynamic evolution of residual stress upon manufacturing Al-based diesel engine diaphragm

Abstract As a thin-walled complex structure, the manufacturing of Al-based diesel engine diaphragms involves casting and heat treatment. Residual stress is introduced during the uneven temperature field in casting and heat treatment, as well as the plastic deformation and cutting heat during mechanical processing. This research investigates the evolution and accumulation models of residual stress in casting and heat treatment for Al-based diesel engine diaphragms using ProCAST and ABAQUS software, combining with the experimental tests. To mitigate residual stress, the optimal parameter combination for casting temperature, knockout temperature, and mold preheating temperature in casting process is explored. The results indicate that the knockout temperature has the most significant influence on casting residual stress, and mold preheating is beneficial for reducing residual stress. Despite improvements, some internal stress concentration areas persist on the knockout casting surface. Furthermore, T6 heat treatment proves to be effective in eliminating more than 50% of the residual stress.

The Influence of Spray Cooling Parameters on Workpiece Residual Stress of Turning GH4169.

To effectively reduce residual stresses in GH4169 workpieces, thus enhancing fatigue strength and operational lifespan, this study investigates the influence of spray cooling parameters on surface residual stresses during GH4169 turning in spray cooling conditions, utilizing both simulation and experimental approaches. A simulation model of residual stresses was established using finite element analysis when GH4169 was cut in spray cooling. The effects of spray pressure and flow rate on residual tensile stresses were analyzed. The analysis reveals that with increasing spray pressure, residual tensile stresses show a decreasing trend, gradually stabilizing. Conversely, with an increasing spray flow rate, residual tensile stresses initially decrease and then increase. The turning experiments of GH4169 were conducted under different spray parameters. After the experiment, the workpiece was sectioned and analyzed for residual stresses using X-ray diffraction instrumentation. The value residual stress measured closely matched those of simulation, with a relative error within 6%, validating the accuracy of the simulation model and confirming the appropriateness of parameter settings. These results contribute to the further promotion of spray cooling technology and facilitate the rational selection of spray parameters.

Analytical and FEM models for thermal analysis and residual stresses using wire arc-based welding and additive manufacturing of SUS304

Analytical and FEM models for thermal analysis and residual stresses using wire arc-based welding and additive manufacturing of SUS304

Novel method for measuring surface residual stress using flat-ended cylindrical indentation

Instrumented indentation is a promising technique for estimating surface residual stresses and mechanical properties in engineering components. The relative difference between the indentation loads for unstressed and stressed specimens was selected as the key parameter for measuring surface residual stresses in flat-ended cylindrical indentations. Based on the equivalent material method and finite element simulations, a dimensionless mapping model with six constants was established between the relative load difference, constitutive model parameters, and normalized residual stress. A novel method for measuring the surface residual stress and constitutive model parameters of metallic material through flat-ended cylindrical indentations was proposed using this model and a mechanical properties determination method. Numerical simulations were conducted using numerous elastoplastic materials with different residual stresses to verify the proposed model; good agreements were observed between the predicted residual stresses and those previously applied in finite element analysis. Flat-ended cylindrical indentation tests were performed on four metallic materials using cruciform specimens subjected to various equibiaxial stresses. The results exhibited good conformance between the stress–strain curves obtained using the proposed method and those from traditional tensile tests, and the absolute differences between the predicted residual stresses and applied stresses were within 40 MPa in most cases.

Experimental and Numerical Study of Membrane Residual Stress in Q690 High-Strength Steel Welded Box Section Compressed Member.

High-strength steel (HSS) members with welded sections exhibit a notably lower residual compressive stress ratio compared with common mild steel (CMS) members. Despite this difference, current codes often generalize the findings from CMS members to HSS members, and the previous unified residual stress models are generally conservative. This study focuses on the membrane residual stress distribution in Q690 steel welded box sections. By leveraging experimental results, the influence of section sizes and welding parameters on membrane residual stress was delved into. A larger plate size correlates with a decrease in the residual compressive stress across the section, with a more pronounced reduction observed in adjacent plates. Additionally, augmenting the number of welding passes tends to diminish residual stresses across the section. Results showed that membrane residual stress adhered to the section's self-equilibrium, while the self-equilibrium in the plates was not a uniform pattern. A reliable residual stress simulation method for Q690 steel welded box sections was established using a three-dimensional thermal-elastic-plastic finite element model (3DTEFEM) grounded in experimental data. This method served as the cornerstone for parameter analysis in this study and set the stage for subsequent research. As a result, an accurate unified residual stress model for Q690 steel welded box sections was derived.

Residual stress model of welded steel L-shaped and T- shaped sections

Steel special-shaped columns, incorporating L, T, or cross-shaped sections, have gained increasing application in modern multi-story and high-rise buildings owing to their benefits in optimizing space utilization and enhancing structural performance. However, the welding manufacturing process induces residual stresses in these steel special-shaped columns, which can adversely affect the stability of the column components. This study conducted experimental research on the residual stress distribution in L-shaped and T-shaped steel columns using the sectioning method, which reveals the residual stress distribution patterns in the two types of steel special-shaped columns. By comparing and analyzing the experimental results with the existing residual stress model for welded sections, a residual stress distribution model for welded L-shaped and T-shaped steel columns is proposed, which fulfills stress self-balanced and is validated through numerical simulation methods. Subsequently, the proposed residual stress distribution model was applied in the numerical analysis of buckling in steel special-shaped columns. The effectiveness and necessity of considering this residual stress distribution model into the stability analysis of steel special-shaped columns are demonstrated by comparing the results with column stability test. The proposed residual stress distribution model significantly enhances the numerical accuracy for steel special-shaped columns, providing a theoretical basis for the stability analysis of such columns.

Modelling of residual stress during curing of a polymer under autoclave conditions and experimental validation

This study develops a multi-scale predictive framework to study the cure kinetics of a polymeric resin under autoclave conditions. The novelty of the study includes evaluation of the cure performance such that the influence of porosity on the residual stress can be interpreted. A representative volume element based finite element model is developed which captures the cure rate and degree of cure under periodic boundary conditions. Resin cure kinetics and heat generation are coded in Fortran via user defined subroutines to capture the non-linear cure response. The autoclave system is simulated as a pressure and thermal load on the resin domain. It is found that an increase of porosity by up to 5%, decreases the level of residual stress by 35% when compared to an ideal configuration, i.e., a no porosity content. The magnitude of residual stress is further validated with XRD results and found to lie within 8%. The proposed model is robust to capture the cure phenomenon of a given thermoset polymer, given the cure kinetic parameters.

Hybrid modeling prediction of residual stresses in turned Ti6Al4V considering frictional contact

Residual stress plays a pivotal role in assessing the surface quality of machined components, influencing characteristics such as fatigue performance, corrosion resistance, and mechanical strength. Ti6Al4V, a critical material in the nuclear sector, the generation of residual stresses during machining has attracted significant attention. A model for variable friction coefficient model is proposed to accurately characterize the complex plastic deformation behavior of the material. This model takes into account variables such as the relative sliding velocity, contact pressure, and temperature. A subroutine has been developed using the VFRIC interface to enhance precise cutting simulation and modeling. Using the friction model, a new hybrid prediction model for surface residual stresses is developed by integrating finite element analysis and analytical methods. The reliability of both the hybrid and friction models is confirmed through the evaluation of cutting forces, chip morphology, and residual stress. The findings suggest that the novel friction model produces simulation results with higher accuracy compared to traditional Coulomb friction models. The variations in cutting force amount to 5.8% and 13.7%, the error in chip serration is 12.4%, and the deviation in predicting the maximum residual compressive stress is 10.3%. This study contributes to the advancement of friction models and methodologies used in predicting residual stress.

A coupled data-physics computational framework for temperature, residual stress, and distortion modeling in autoclave process of composite materials

It is challenging to obtain the full-field temperature profile during autoclave processes to control the temperature uniformity and minimize the residual stress and distortion of cured composite structures. This paper proposes a coupled data-physics computational framework for full-field temperature reconstruction and the subsequent residual stress/distortion modeling by using limited monitoring temperature data. Firstly, a Long Short-Term Memory (LSTM) model is developed for full field temperature reconstruction. In this LSTM model, a cross-recombination method is proposed to maximize the value of monitored temperature data. The method effectively cuts through the bottleneck of neural network training with limited labeled data. The LSTM model’s prediction stability is enhanced based on the mean-teacher and ensemble learning strategy. To train and validate the proposed method, we perform experiments using an autoclave at the National Institute for Aviation Research (NIAR). The LSTM model’s accuracy is assessed by comparing its predicted results with the thermocouple (TC) data from measurements and high-fidelity simulation data from computational fluid dynamics (CFD). The study shows that the proposed LSTM model can effectively reconstruct the full-field temperature using limited monitoring data and significantly improve accuracy and efficiency compared with the CFD-based counterpart. Then, we create a coupled data-physics computational framework by embedding the data-driven LSTM model into a physics-based thermo-mechanical finite element model to predict residual stress and distortion. The simulation results show that the coupled data-physics framework provides an effective way for process-to-performance modeling and simulation of autoclave curing processes.

A framework to efficiently simulate the cyclic variation of the residual stresses induced by chip formation in machining of Ti-6Al-4 V alloy

Residual stresses is a key part of surface integrity, having a strong influence on the functional performance and lifespan of components. Advances in modeling of machining-induced residual stresses are fundamental to achieve more accurate predictions. Due to the low computational efficiency and the lack of consideration of the whole residual stress formation process, a framework to simulate the residual stress in the machining of Ti-6Al-4 V titanium alloy using CEL (Coupled Eulerian and Lagrangian) and Lagrangian approaches is proposed. A model of the cutting and workpiece unloading processes is simulated using CEL approach and explicit time integration scheme. Then, a model of the cooling process of the workpiece is developed in order to calculate the residual stresses. To improve computation efficiency and to reduce the effects of cumulative errors, this model is simulated using Lagrangian approach and implicit time integration scheme. Data transfer between these two models is performed by combining a strategy of data transfer and mesh rebuilding. The cutting force and residual stress are obtained by simulation with average errors of 18% and 21%, respectively. The predicted and measured thicknesses of the layer are reasonable well predicted. The computational time of proposed approach can be greatly reduced from 81 h to 5.3 h by comparison with traditional one. This framework was then used to investigate the cyclic variation of the residual stress along the cutting direction, which is due to the cyclic nature of the chip formation process.