Calculation Of Residual Stresses Research Articles

Stress and residual stress distributions in plane strain bending

Stress and residual stress distributions in bending are important in calculating springback and loading capacity of a sheet-metal bending part. Great differences have been found in springback prediction with the same input (benchmark problems) among different researchers. In order to find out the root cause of these differences, stress and residual stress calculation methods in plane strain bending are briefly reviewed or developed. The influence of deformation theory and incremental theory, repeating bending, unbending and re-bending, cyclic material models and springback calculation methods on the stress or residual stress distributions are examined and shown to be large. This emphasizes the importance of careful selection of these variables in a simulation model in addition to other general input variables, such as material properties, tool geometry and friction condition. This fact also helps to explain the great differences among different research results, and presents a challenge to both the programmers and the users of finite element packages.

Diffusion processes and mechanics of materials

Within the framework of continuum mechanics, we investigate the interdependent processes of strain and diffusion. By solving a wide class of initial-value and boundary-value problems concerning a physicomechanical state of elastic and viscoelastic bodies, we establish kinetic regularities of the interaction of structural and functional materials with working and technological media. We propose approaches to the calculation of residual stresses under conditions of multicomponent diffusion, phase transformations, and chemical reactions. We emphasize the importance of a consistent and rigorous consideration of properties of structural materials for the construction of their physicomathematical models. Tendencies and prospects of the development of investigations in this direction are evaluated.

Estimation of residual stresses in SiC/Ti 15-3 composites and their relaxation during a fatigue test. Part I: Presentation of the models

Different models for the calculation of residual stresses induced by cooling down from elaboration process in SiC/Ti-15-3 composite were presented. First of all, an analytical model (derived from those of Eshelby and of Mikata and Taya) already used for ceramic matrix composites is explained. It is a suitable method for elementary composites but we present an extension of this model to real (1D) composites. Then, we also briefly present the finite model using MARC anc MENTAT softwares. Finaly, an analytical model to predict the evolution of TRS during a fatigue test is detailed. The part II of the paper will present the results obtained using all these differents models.

Calculation of Residual Stress in F-Doped Depressed Inner Cladding (DIC) Fiber

AbstractThe analytic calculation and the measurement of thermal stresses have been performed for concentric three layered structures of a fiber-core, inner, and outer cladding. Especially the effects of F-doped inner cladding on the residual stress have been parametrically studied.

Martensite formation and residual stresses around railway wheel flats

A finite element (FE)-based computational model is developed for the calculation of residual stresses in steel as induced by a local thermal shock. Subroutines to handle phase transformations and constitutive behaviour including volumetric expansion and transformation-induced plasticity are added to a commercial FE code. Sliding contact problems with application to railway technology are studied. Six examples of wheel flat formation are investigated in detail. In all of them rather high tensile stresses are found in the wheel rim in a domain below the top layer of phase transformations. For those combinations of train speed, wheel load and sliding duration, where the brittle martensite phase is found, surface cracks are likely. The predicted tensile stresses may propagate these cracks further into the rim material and thus cause spalling.

Residual stresses, shrinkage, and warpage of complex injection molded products: Numerical simulation and experimental validation

AbstractA numerical simulation model for predicting residual stresses and residual deformations which arise during the injection molding of thermoplastic polymers in the post‐packing stage has been developed. A thermoviscoelastic model with volume relaxation is used for the calculation of residual stresses. The finite element method employed is based on the theory of shells as an assembly of flat elements. This theory is well suited for thin injection molded products of complex shape. The approach allows the prediction of residual deformations and residual stresses layer by layer like a truly three‐dimensional calculation, while reducing the computational cost significantly. The hole drilling technique is used to measure the residual stresses across the thickness of the product. A three‐dimensional laser digitizing system, an image processing technique and a dual displacement transducer system are used to measure the warpage. Experiments are carried out on polycarbonate and high density polyethylene parts. Numerical results are in qualitative agreement with experimental observations, i.e., the skin of the box is surrounded by a compressive region while the core region is in traction. The trend of both the experimental and the predicted residual stress profiles is close. Different examples are presented to illustrate the influence of the geometrical complexity of the shape on the final deformations and residual stresses. The influence of the mold temperature on residual stresses and warpage is also analyzed.

Processing of laminated hybrid ceramic composites

The thermoelastic response of ceramic composite laminates was studied in order to optimize their design and fabrication. Laminated ceramic composites were fabricated with induced thermal residual stresses resulting from subsequent cooling from elevated processing temperatures. Samples were fabricated by tape casting laminae of different compositions and then bonding them together by hot pressing to form the finished laminate. These laminates were analyzed to better understand the process occurring during hot pressing that produced bonded and consolidated composites. Calculated laminate properties were found to be comparable to measured values. Microprobe elemental analysis was used to determine the interlaminar and intralaminar reactions occurring during fabrication. X-ray diffraction stress analysis was used to verify predicted residual stress calculations. Residual stresses and stress-driven reactions were found to be contributing factors in the resulting microstructural variations found within the composites.

An approximate algorithm for elastic-plastic two-dimensional rolling/sliding contact

In this paper, we introduce an approximate algorithm for two-dimensional elastic-plastic rolling/sliding line contact which admits arbitrary forms of kinematic hardening models for nonproportional cyclic plasticity. The new hydrid scheme combines attractive features of the McDowell and Moyar [1,2] and Sehitoglu and Jiang [3,4] approaches, enabling prediction of subsurface cyclic plasticity and residual stresses for loading conditions ranging from small to large cyclic plastic-strain ranges. The approach is compared with finite element calculations of residual stresses and subsurface cyclic plasticity for both high and low strength alloys. A comparison is presented with the previous McDowell-Moyar algorithm in terms of the prediction of subsurface residual stresses within the half space over a wide range of loading conditions.

An Axisymmetric Method of Elastic-Plastic Analysis Capable of Predicting Residual Stress Field

Linear elastic solution of an axisymmetric boundary value problem is used as a basis to generate its inelastic solution. This method treats the material parameters as field variables. Their distribution is obtained as a part of solution in an iterative manner. Two schemes of updating material parameters are discussed and compared. A procedure for calculation of residual stress field is presented. Application of the method to autofrettage is presented. Residual stress calculation based on actual material curve, isotropic and kinematic hardening models, and variable Bauschinger effect factor (BEF) is carried out. It is concluded that consideration of dependency of BEF on plastic strain makes significant changes to residual hoop stress near the bore for low-level autofrettage. However, this dependency is insignificant for high-level autofrettage. Results obtained here are shown to be in good agreement with experimental and finite element results.

アルミナ分散銅強化チューブ法Nb<SUB>3</SUB>Sn線の応力歪効果

In order to fabricate a large-bore, high-field magnet which achieves a low coil weight and volume, a high strength compound superconducting wire is required. For those demands we have developed the reinforced Nb3Sn wire using alumina dispersion strengthened copper (alumina-Cu) as a reinforcement material and the tube process of the Nb3Sn wire fabrication.The ductility study of the composites which consisted of the reinforcement, Nb tube, Cu, and Cu clad Sn brought a 1 km long alumina-Cu reinforced Nb3Sn wire successfully. Using fabricated wires measurements and evaluations of critical current density as parameters of magnetic field, tensile stress, tensile strain, and transverse compressive stress, and those of stress-strain curves at 4.2 K were performed.They showed superior performance such as high 0.3% proof stress (240 MPa at 0.3% strain) and high maximum tolerance stress (320 MPa) which were two times as large as those of conventional Cu matrix Nb3Sn wire. The strain sensitivity parameters were obtained for the reinforced Nb3Sn wire and the Cu matrix one using the scaling law. Residual stress of the component materials caused by cooling down to 4.2 K from heat-treatment temperature was calculated using equivalent Young’s modulus, equivalent yield strength, thermal expansion coefficient and other mechanical parameters. Calculated stress-strain curves at 4.2 K for the reinforced Nb3Sn wire and the Cu matrix one based on calculation of residual stress, had good agreement with the experimental values.

Measurement and calculation of residual stresses after die forging

For die forgings, fabricated from steels Ck 45, 42 CrMo 4 and 38 MnSiV S 6 3, TTT and CCT diagrams were determined, and after different heat treatments, measurements of mechanical properties, fatigue strength and residual stresses were carried out. The diameter of the specimens after the forging process was 32 and 45mm. The residual stresses after quenching between -450 and +160N/mm 2 could be reduced to about 60N/mm 2 by tempering up to 620°C. The fatigue strength in the range of 300N/mm 2 depends more on the strength than on the residual stresses. Calculations with the program Antras-Thepla correlate well with the measured microstructures and residual stresses. This shows that the materials and processing data used for the calculation are conform to real processes.

Squeeze cast aluminium reinforced with mild steel inserts

The bonding of a mild steel insert to an Al-7Si alloy during squeeze casting has been studied for a range of processing conditions. Assessment of the mild steel/Al-7Si alloy interface shear strength has been made with a push-out test, and the results have been correlated with microstructural observations and residual stress calculations. Uncoated inserts do not exhibit any significant reaction with Al-7Si because of rapid cooling of the melt during squeeze casting, giving a low interface shear strength of ∼ 30 MPa. Preheating the inserts to 900°C slightly improves the interface shear strength to ∼ 45 MPa, but reaction between the steel and Al-7Si is prevented by the formation of an Fe3O4 magnetite layer on the steel surface. Inserts hot-dipped in molten Al-10Fe before squeeze casting have a much greater interface shear strength of ∼ 110 MPa, with failure in the Al-7Si matrix rather than at the steel/Al-7Si interface. Inserts vacuum plasma spray coated with titanium have the greatest interface shear strength of ∼ 130 MPa, without any interface reaction, because of mechanical keying of the rough splat-quenched titanium surface combined with high residual stresses in the Al-7Si matrix.

Considering Stress-Phase Transformation Interactions in the Calculation of Heat Treatment Residual Stresses

Considering Stress-Phase Transformation Interactions in the Calculation of Heat Treatment Residual Stresses

Calculated elastic constants of wide band gap semiconductor thin films with a hexagonal crystal structure for stress problems

The Young's modulus, E, and Poisson's ratio, v, can be used for theoretical calculation or experimental determination of residual stresses arising during the growth of wide band gap semiconductor thin films. In this paper, a generalized expression for v and E (1−v) for the hexagonal closed packed (hcp) structure common to wide band gap semiconductors has been given for the first time. In addition, the specific expressions for E, v, and E (1−v) are given for directions within the c and r planes in the hcp structure. These elastic constants are found to be invariant within the c plane but not within the r plane. Numerical values for these elastic constants are computed and listed for 6H-SiC, Al 2O 3, and AlN.

Thermal residual stresses in a functionally graded material system

A one-dimensional calculation of thermal residual stresses, arising from the fabrication of a Functionally Graded Material (FGM) system, is presented. As a first step, calculations have been limited to the linear elastic case. The FGM system consists of ceramic (Al 2O 3) and metal (Ni) phases varying with distance in one direction. Several functional forms of gradation of constituents were examined to arrive at the optimum profile giving the minimum residual stress level. A linear variation in composition from fully ceramic to fully metal showed the least residual stress. Residual stresses were found to increase when fully ceramic and/or fully metal regions are included in the structure, adjoining the graded zone. The character (tension or compression) of stresses is dependent on the functional form of gradation. A low residual stresses state close to that of the continuously graded structure can be achieved also in a multilayer FGM system having several layers (typically > 11) of constant composition. The effects of temperature dependent elastic and thermal expansion characteristics of constituents on residual stress were found to be small.

Elastic Calculation of Residual Stresses in Injection Molding

Abstract A calculation of residual stresses in injection molding using a 2-D description of the geometry is presented. The polymer follows an elastic behavior law. The thermal shrinkage and the frozen-in pressure when a layer solidifies are taken into account. A calculation of the pressure in the liquid areas after the gate is frozen is presented. A simplified mold deformation model is introduced and its influence on residual stresses is shown. Results are presented for a polystyrene injected in a square plaque.

Calculation of residual stresses in case-hardened SAE5115 steel cylinders

The development of stresses for five differently case-hardened SAE5115 steel cylinders with variable surface carbon mass contents c S and carburization depths CD during single hardening are calculated. The carbon profiles and the retained austenite distributions in the near-surface material areas are approximated in a stepwise manner. Exemplarily, in the middle plane of cylinders with c S = 0.5% C (CD = 0.07 mm) and 1.1% C (CD = 0.2 mm), the local axial stresses at the surface, at four near-surface points and in the core are described during the hardening process up to temperature balance. The influence of c S and CD on the surface tangential residual stress values along the casing of the cylinders is outlined. Also the depths distributions of the tangential residual stresses in the middle plane are presented for differently carburized cylinders. At c S = 11% C = const. the distance of maximum compressive residual stresses beneath the surface as well as the thickness of the compressed surface and the distances with the largest tensile residual stresses increase with increasing CD

Prediction of residual flow and thermoviscoelastic stresses in injection molding

A general model for predicting the total residual stresses generated during filling and cooling stages of injection-molded parts has been developed. The model takes into account the phenomena associated with non-isothermal stress relaxation. The main hypothesis in our approach is to use the kinematics of a generalized Newtonian fluid at the end of the filling stage as the initial state for the calculation of residual flow stresses. These stresses are calculated using a single integral rheological model (Wagner model). The calculation of stresses developed during the cooling stage is based on a thermoviscoelastic model with structural relaxation. Illustrative results emphasizing the effect of both the melt temperature and the flow rate during the filling stage are presented.

塑性予ひずみを与えたAl<SUB>3</SUB>Niウィスカ/Al系複合材料中の格子ひずみの中性子回折による測定

The time-of-flight (TOF) analysis method in neutron diffraction has been applied to the study of residual stress states associated with the mechanisms of back-stress hardening and diffusional recovery in a short fiber-reinforced metal matrix composite. The composite examined was an experimental model system, Al3Ni whisker-reinforced aluminum, produced by directional solidification of the Al-6.2 mass%Ni eutectic alloy. It was cold-swaged and then annealed, so that very long (essentially continuous) whiskers changed into short fiber morphologies. Incremental strain amplitude tension-compression tests were carried out at room temperature and 500°C up to the total strain of 0.3% with final unloading from the tension side. Neutron diffraction experiment was subsequently performed to measure residual lattice strains in the deformed specimens, together with the as-annealed one as the reference material. A couple of detectors were properly arranged so as to make simultaneous measurements of lattice spacings in both the axial and transverse directions of the specimens. From the set of diffraction data, residual lattice strains and hence, residual stresses in both the axial and transverse directions were fully determined for the alminum matrix in the specimens deformed at room temperature and at 500°C; however, the corresponding residual stress states for the Al3Ni whiskers were indeterminable because of incomplete diffraction data due to the effect of preferred orientation of the Al3Ni whiskers. The results are discussed in light of independent calculations of residual stresses based on a micromechanics-based analysis of the stress-strain data in tension-compression tests.

The Calculation of Residual Stresses in Worn Surfaces

An elastoplastic model for calculating the residual stresses caused by the indentation of a semi-infinite solid by aflat punch is developed to allow calculation of the residual stresses left in a soft surface after it has been rubbed by a hard wedge. Despite the simplifications used, the model predicts to within 20 per cent the magnitude of the residual stresses produced by the gentle grinding of metals. It also predicts the essential features of the stress field and direction of crack propagation in some recent experiments on the sliding of steel wedges on aluminium.