Calculation Of Residual Stresses Research Articles

Numerical Simulation and Experimental Study of Warpage of Injection-Molded Parts

: The accurate prediction of warpage of injection-molded parts is important to achieve successful mold design and processing parameters settings with high precision. A numerical simulation model for predicting residual stress and warpage that arise during the injection molding of thermoplastic polymers in the packing and cooling stages has been developed. A thermorheologically simple viscoelastic model was used for the calculation of residual stress. The finite element method for warpage simulation was based on the theory of shells as an assembly of flat elements that are formed by combining the constant strain and the discrete Kirchhoff triangular element. This theory is well suited for thin injection-molded products of complex shape. Experiments on a flat plate were also carried out to study the effect of processing parameters on warpage. The simulation results were also compared with the experimental data for verification of the developed program. It was found that the predictions were in agreement with experimental data, especially in qualitative analysis.

Expedient Evaluation Method of Residual Stress for Viscoelastic Laminated Bodies

A simplified equation, designed to obtain inter-layer residual stress arising when thermal load was provided to a viscoelastic laminate beam consisting of various materials, was proposed, and reasonableness of the equation was examined through comparison with exact solution based on thermal viscoelastic analysis. The proposed simplified equation is composed of the glass transition temperature, the rubber transition temperature, the elastic coefficient, and the linear expansion coefficient of the component material. Based on this composition, it has been clarified that the equation allows calculation of inter-layer residual stress in laminated beams. Because the simplified solution of the inter-layer residual stress that is generated in viscoelastic laminate beams is well consistent with the precise solution derived from the basic thermal viscoelastic formula, the rationality and efficiency of the simplified solution have been revealed.

Calcul des contraintes résiduelles dans les zones d'assemblage de plaques en verre trempé

Ce travail porte sur l'utilisation du verre comme véritable matériau de structure et concerne plus particulièrement le calcul des contraintes résiduelles de trempe autour des zones d'assemblage par insertion d'un connecteur métallique au sein de plaques trouées et chanfreinées pour la prédiction de la résistance de tels assemblages. Des simulations numériques par la méthode des éléments finis du procédé de trempe sont menées pour le calcul des contraintes transitoires et résiduelles près des bords de plaques de verre (calculs 2D) et près de trous chanfreinés (calculs 3D). Le verre est considéré comme un matériau viscoélastique, le modèle de Narayanaswamy est utilisé, il prend en compte les phénomènes de relaxation de contraintes d'origine visqueuse et structurale. Une difficulté provient de la description correcte des transferts de chaleur pendant la trempe qui est d'importance majeure pour la prédiction des contraintes résiduelles. La convection forcée due au soufflage de l'air et le rayonnement sont modélisés, le caractère semi-transparent du verre est pris en compte. Les coefficients de convection forcée dans les zones bords sont identifiés expérimentalement. Les résultats de prédiction des contraintes résiduelles de trempe sont comparés à des résultats de mesures photo-élastiques. Ce travail permet l'optimisation de la géométrie de la plaque de verre pour un renforcement maximal dans la zone d'assemblage.

Residual Stress Computation in Bent Profiles Using Analytical Approaches

Approaches to the theoretical treatment and calculation of residual stresses without the utilization of experimentally determined values are made for different reasons. First, the experimental determination of residual stresses requires the use of very expensive devices and is very time-consuming. Second, the experimental determination cannot be carried out before the manufacturing or further processing of the parts to be measured has been finished. Therefore, residual stresses are not recognized before the workpieces are actually manufactured and a pre-estimation, still in the design phase, of the effect of these stresses on the workpiece properties is not possible. In this paper, an improved computation method for the determination of residual stresses within bent profiles is presented. The computation algorithm is based on analytical approaches taken from the literature. The residual stress computation is integrated into a semi-analytical process simulation that allows the fast determination of process and product data for the manufacturing of profile structures.

Measurement of Fiber-scale Residual Stress Variation in a Metal-matrix Composite

The crack compliance, or slitting, method was used to measure a localized depth profile of residual stresses in a metal-matrix composite. The composite consisted of a matrix of Kanthal, a Fe–Cr–Al refractory alloy, reinforced with continuous uniaxial tungsten fibers. The stress measurements involved successively deepening a narrow slit between the fibers in the matrix, and measuring the resulting deformations with a surface strain gage. The depth profile of the in-plane residual stress components was determined from the measured strains using an eigenstrain-based extension of the residual stress calculation scheme normally used for slitting measurements. To validate some of the eigenstrain assumptions, the measured residual stresses were compared with the predictions from a thermomechanical finite element model. The model used a mesh of the actual fiber arrangement in the composite specimen rather than the commonly used unit-cell model. Compared to other techniques for measuring residual stresses in composites, the slitting measurements provided spatial resolution to a small fraction of the fiber diameter, which is useful when validating a thermomechanical model. Coincidentally, this is the first reported slitting method measurements of shear residual stresses.

Calculation of residual thermal stress in GaN epitaxial layers grown on technologically important substrates

A detailed investigation of residual thermal stress and misfit strain in GaN epitaxial layers grown on technologically important substrates is performed. The thermal stress is low when GaN is grown on AlN, SiC and Si, and relatively higher when Al2O3 substrate is used. The stress is compressive for AlN and Al2O3 and tensile for Si and SiC substrates. Residual thermal stress analysis was also performed for three layer heterostructures of GaN/AlN/6H-SiC and GaN/AlN/Al2O3. The stress remains the same when a sapphire substrate is used with or without an AlN buffer layer but reduces by an order of magnitude when a 6H-SiC substrate is used with an AlN buffer layer.

Modelling and analysis of a deep-drawing operation: key factors for successful comparisons between experimental and simulated results

The objective is to determine the finest finite element simulations of deep-drawing operations, including spring-back effect, until the occurrence of strain localisation.This paper insists on two aspects that have a major influence on the results of the simulations: precise determination of the equivalent stress–equivalent strain relationship and description of boundary conditions.The stress–strain curve has been determined using duplicate analysis of tensile test. The classic extensometric strain measurement is compared with the measurements of strain with an automatic analysis of digital images caught at various deformation stages. The measurements by image analysis allow the determination of local strains and give them a more precise determination for the high strains.As to boundary limit problems managed with explicit algorithm, success mainly depends on the control of the process that has to remain in quasi-static range.In order to analyse the accordance of the results of the simulation and then obtained by the experiment, the precise method of residual stress calculation is elaborated for the case of the original tensile test: simultaneous loading and subsequent unloading to the equilibrium state of assembly of three samples with different lengths.The comparisons of the experimental and numerical results are very satisfactory.

Residual stresses computation in a grinding process

Grinding induces residual stresses, which can play an important role on the fatigue and wear resistance of the component. It is generally expected that conventional grinding leads to tensile residual stresses, while compressive stresses are obtained with high speed grinding (HSG). In this paper, a finite element thermomechanical model for the calculation of residual stresses induced by a surface grinding process on a steel workpiece (AISI 52100) is presented. A model giving the energy conducted as heat in the workpiece as a function of the grinding wheel speed, the workpiece speed, and the cutting depth is proposed. This model is available for conventional grinding for wheel speeds less than 120 m s −1. It is shown that, for such grinding conditions, the simulation leads to tensile residual stresses. Moreover, the computation shows that the temperature in the grinding area increases when the peripheral wheel speed increases too. So it is expected that for wheel speeds corresponding to HSG (>120 m s −1), the surface temperature can reach values leading to an austenitic transformation and therefore, during cooling, the workpiece can be subjected to a superficial quenching leading to compressive residual stresses. Finally, the present paper shows that the metallurgical phenomena in the grinding area must be surrounded and must be taken into account in future models.

Nonlinear finite element calculations of residual stresses in dislocated crystals

A finite element algorithm for the determination of both residual stresses and lattice orientation in dislocated crystals is presented. The applied theoretical approach is based on the continuum theory of dislocations. Due to the compatibility condition, an initial plastic distortion field has been used to introduce an elastic incompatibility corresponding to the assumed dislocation density tensor field. The presented method gives the possibility to develop a numerical code suitable for determination of the stress field and lattice orientation. Two numerical examples are given: a low-angle dislocation wall and a subboundary structure. The method can be applied especially to dislocation sets composed of a few groups of monomial dislocations.

X-ray diffraction residual stress calculation on textured La2/3Sr1/3MnO3 thin film

Residual stresses and texture in La2/3Sr1/3MnO3 (LSMO) thin films have been investigated. The films were deposited on (100) LaAlO3 (LAO) and (100) MgO single crystals by liquid delivery-metal organic chemical vapor deposition (LD-MOCVD). X-ray diffraction (XRD) pole figures showed (001)LSMO//(001)LAO and (001)LSMO//(001)MgO preferred orientation. Residual stresses were calculated using a modified sin2ψ method, crystallite group method (CGM), assuming a biaxial stress state. Compressive stresses on the order of 224 and 1150MPa were obtained for LSMO films deposited on LAO (LSMO/LAO) and MgO (LSMO/MgO), respectively.

Measurement of non-uniform residual stresses by combined Moiré interferometry and hole-drilling method: Theory, experimental method and applications

Hole-drilling method is one of the most convenient methods for engineering residual stress measurement. Combined with moire interferometry to obtain the relaxed whole-field displacement data, hole-drilling technique can be used to solve non-uniform residual stress problems, both in-depth and in-plane. In this paper, the theory of moire interferometry and incremental hole-drilling (MIIHD) for non-uniform residual stress measurement is introduced. Three dimensional finite element model is constructed by ABAQUS to obtain the coefficients for the residual stress calculation. An experimental system including real-time measurement, automatic data processing and residual stresses calculation is established. Two applications for non-uniform in-depth residual stress of surface nanocrystalline material and non-uniform in-plane residual stress of friction stir welding are presented. Experimental results show that MIIHD is effective for both non-uniform in-depth and in-plane residual stress measurements.

Residual stress induced by solidification of thermoviscoelastic melts in the postfilling stage

Injection moulding is a process where polymer melt is injected into a mould cavity, and solidifies to form a plastic part. Residual stress usually develops during the solidification of the melt in the postfilling stage. This study use a simple thermoviscoelastic model to calculate the residual stress developed in the postfilling stage. Based on the calculation of the injection moulding process, the temperature and pressure histories in the postfilling stage can be determined, and used to calculate the developed stress field. The model divides the thickness into two regions, liquid and solid. Residual stress calculation is applied in the solid region, while the liquid region is kept at the local melt pressure without any strain.

On the Residual Stress and Shrinkage in Injection Compression Molding

Abstract Injection compression molding is a process having a compression action in the filling or postfilling stages. This process is suitable for molding of parts with precision features. The success of an injection compression molding process relies on proper design of the mold and selection of process conditions. The main scope of this study is to develop an analysis tool for the residual stresses and shrinkage of an injection compression molding process. A simple thermoviscoelastic model was used to calculate the stress and relaxation developed in the postfilling stage. The model divides the thickness into two regions, glassy and rubbery phases. Residual stress calculation is applied in the glassy region, while the rubbery region is kept at the melt pressure without any strain because of the fast relaxation in this region. The resulted in-mold stress fields are used to calculate the part shrinkage after demolding. The effects of the compression force on the residual stresses and shrinkage of a molding part were also investigated. Higher compression force tends to reduce the part shrinkage but induces a higher level of residual stresses.

Hydraulic Versus Swage Autofrettage and Implications of the Bauschinger Effect

A hybrid method is presented which permits calculation of residual stresses in a swage autofrettaged tube including Bauschinger effect. The results are generally supported by three types of available experimental evidence by comparing “equivalent” swage and hydraulic autofrettage tubes having the same level of overstrain. Radial slitting of the swaged tube is predicted to show a greater opening angle than its hydraulic equivalent. Fatigue lifetime of the swaged tube is predicted to be significantly higher than the hydraulic case. Re-pressurization of the equivalent tubes is predicted to produce initial re-yielding at the same pressure in both cases. Analysis of results shows that permanent strains in the swaged tube are expected to appear at a pressure level below that for the hydraulic tube.

FEM simulation of residual stresses induced by laser Peening

Benefits from laser Peening have been demonstrated several times in fields like fatigue, wear or stress corrosion cracking. However, in spite of recent work on the calculation of residual stresses, very few authors have considered a finite element method (FEM) approach to predict laser-induced mechanical effect. This comes mainly from the high strain rates involved during LP (10 6 s -1 ), that necessitate the precise determination of dynamic properties, and also from the possible combination of thermal and mechanical loadings in the case of LP without protective coatings. In this paper, we aim at presenting a global approach of the problem, starting from the determination of loading conditions and dynamic yield strengths, to finish with FEM calculation of residual stress fields induced on a 12% Cr martensitic stainless steel and a 7075 aluminium alloy.

Calculation of Residual Stresses of Cross-Ply Laminates

Residual stresses in composite laminates are primarily caused by the difference between the volume change in the polymer matrix and the reinforcing fibres. In resins, volume changes are produced by the chemical shrinkage during the cure and by thermal expansion through the whole manufacturing process. In the laminate plane the resin volume change is restricted, which causes quite large dimension change in thickness direction. In addition, global and local structures of the laminate are engaged such that they together determine the laminate temperature, degree of cure and dimension change histories. Unlike most existing work, which model the laminates either in global or in local level only, a calculation procedure of the residual stresses is developed using both the global and the local model. A perfect coupling between the models has not been reached, but the residual stresses in the local structure are obtained by using the results of the global structure as boundary conditions. The computations address that the local stresses in the resin and fibres differ remarkably from the macro scale stresses in the laminate layers. Also, it is necessary to model the laminate in three dimensions, because the residual stresses in the resin are closely related to the changes in the laminate thickness.

EDM simulation: finite element-based calculation of deformation, microstructure and residual stresses

A finite element-based model for the electric discharge machining (EDM) process is presented. The model uses process parameters such as power input, pulse duration, etc., to predict the transient temperature distribution, liquid- and solid-state material transformation, and residual stresses that are induced in the workpiece as a result of a single-pulse discharge. An attractive feature of the model is its ability to predict the shape of the crater that is formed as a result of the material removal. The model has been validated using experimental data, wherever possible. Extending the model to simulate the effects of multiple pulses will be undertaken in the near future.

On the Improvement of Calibration Coefficients for Hole-Drilling Integral Method: Part II—Experimental Validation of Calibration Coefficients

Experimental validation of the calibration coefficients for integral hole-drilling method obtained from an improved three-dimensional FEM model was achieved using bending test of a cantilever beam. The experimental setup is a simple yet accurate method to validate the calibration coefficients obtained by a three-dimensional FEM model. With this experiment, we also validate the adequacy of the criterion applied for thin or thick plates in a previous work. The relieved stresses calculated from the calibration coefficients of the three-dimensional FEM model were compared with those calculated from two-dimensional model calibration coefficients. The results show that the accuracy of relieved stress calculation has been greatly improved as the calibration coefficients based on a three-dimensional model are used for integral hole-drilling method. Significant error in the residual stress measurement and calculation could be arisen if calibration coefficients for integral hole-drilling method were not chosen correctly for corresponding thin plate or thick plate cases according the results of the bending test of cantilever beam. A transitional dimensionless thickness was proposed by examining the calculated relieved stresses obtained from the calibration coefficients for different plate thickness. The probability bounds of relieved stress corresponding to both cases were also calculated to further reveal the improvement of the calibration coefficients obtained from the three-dimensional model.

A New X-ray Method For Residual Stress Evaluation In Coatings

Transition metal nitride coatings films such as TiN or ZrN have been extensively studied for industrial applications. Residual stresses of the coatings generally affect the mechanical behaviour and the corrosion resistance and hence the performance of the product. The development of new, fast and simple methods for the assessment of residual stresses is then of great importance for coating technologies. In this paper a new method for X-ray residual stress calculation is proposed. Ths method is based on the analysis of the Debye rings obtained with 2D detectors. In particular, preliminary results concerning ZrN decorative coatings that are exposed to hghly corrosive environments are shown. For the structural, morphological and mechanical characterisation of the ZrN coatings, glancing incidence X-ray diffraction (GIXRD) experiments, nanoindentation, and optical and scanning electron microscopy (SEM) analyses were performed.

Numerical Simulation for Effects of Injection Mold Cooling on Warpage and Residual Stresses

The dimensions quality of the injection‐molded parts is the result of a complex combination of material, part, and mold designs and process conditions. In this article, warpage prediction relies on the calculation of residual stresses developed during the molding process. The solidification of a molten thermoplastic between cooled parallel plates is used to model the mechanics of part warp in the injection‐molding process. Flow effects are neglected, and a thermorheologically simple thermoviscoelastic material model is assumed. The warp and residual stresses numerical simulation with finite element method (FEM) is time dependent. At each time step, the material properties can be temperature and pressure dependent. Mold temperature or mold‐cooling rate effects on part warp have been numerically predicted and compared with experimental results. By showing the mold‐cooling effects, it was concluded that mold cooling has a significant effect on part warpage, and mold‐cooling parameters, such as mold temperature, resin temperature, cooling channels, etc., should be set carefully.