Numerical aspects of finite element simulations of residual stresses in metal matrix composites

When a metal matrix composite (MMC) is cooled down from the fabrication or annealing temperature to room temperature, residual stresses are induced in the composite due to the mismatch of the thermal expansion coefficients of the matrix and reinforcement. A thermomechanical model describing these processes is presented considering that the reinforcement component has a thermo‐elastic behaviour and that the matrix material exhibits a thermo‐elastoviscoplastic behaviour. The model is implemented with a semi‐implicit forward gradient finite element method algorithm and the resulting code is used to perform numerical simulations and calculate thermally induced residual stress fields in MMCs. Several tests are performed on a continuously reinforced MMC and a short cylindrical particle MMC in order to optimize the algorithm and define its governing parameters. Good agreement was obtained with results from other authors. Copyright © 2001 John Wiley & Sons, Ltd.     

Evaluating stress intensity factors due to weld residual stresses by the weight function and finite element methods

This paper presents a study on the application of the weight function and finite element methods to evaluate residual stress intensity factors in welded test samples. Three specimen geometries and various residual stress profiles were studied. Comparisons of the two different methods were made in terms of the accuracy, easiness to use, conditions and limitations. Calculated residual stress intensity factors by the two different methods are in general in good agreement for all the configurations studied. Computational issues involved in executing these methods are discussed. Some practical issues are also addressed, e.g. treatment of incomplete or limited residual stress measurements, influence of transverse residual stresses, and modelling residual stress in short-length specimens. The finite element method is validated by well-established weight functions and thus can be applied to complex geometries following the procedures recommended in this paper.     

An orthogonal residual procedure for non-linear finite element equations

A general and robust solution procedure for non-linear finite element equations with limit points is developed. At each equilibrium iteration the magnitude of the load is adjusted such that the residual force is orthogonal to the current displacement increment from the last equilibrium state. The method implements the physical condition that the orthogonal residual force will neither increase nor decrease the magnitude of the current displacement increment vector. The orthogonality condition is formulated directly in terms of conjugate variables and therefore does not contain any scaling parameters. Passage of load and displacement limit points is discussed as well as the relation to line search, minimum residual, and are-length methods. The method is illustrated by two examples.     

Thermomechanical analysis of residual stresses in brazed diamond metal joints using Raman spectroscopy and finite element simulation

Thermal residual stresses are one of the crucial parameters in engineered grinding tool (EGT) life and its consistency. Predicting failure of brazed diamond metal joints in EGTs is related to analyzing the thermal residual stresses during the cooling process. Thus thermal residual stresses have been simulated in a model with realistic materials properties, for instance isotropic hardening and a hyperbolic-sine creep law for SS316L and the silver–copper–titanium active filler alloy, named Cusil ABA™. Also, special modeling techniques such as tie constraint and sub-modeling have been used to model an intermetallic layer titanium-carbide (TiC) with dimensions in nanometers, where the rest of the model’s dimensions are in millimeters. To verify the simulated stress state of the diamond, Raman-active optical phonon modes at three different paths in the diamond were measured. As the experiments with Raman spectroscopy (RS) do not deliver stress components, the solution is to directly compute the peak shift of Raman spectrum. The splitting in phonon frequencies and the mixing of phonon modes contain information about the thermal residual stresses in the diamond. Finally the shift in the phonon frequencies was calculated from the different numerical residual elastic strain components and compared to the experimental results.     

Determination of residual stresses in welded components by finite element analysis

The continued safe and reliable operation of plant invariably has to consider the assessment of defects in welded structural components. This requires some estimate of the residual stresses that have developed during the welding fabrication process. There is an increasing use of computational weld mechanics to evaluate residual stresses and this paper describes the development of guidelines for using finite element analysis, which are now incorporated into the EDF Energy R6 defect assessment procedure, to determine stresses for use in the procedure. Prior to use in assessment the predicted results should be validated by comparison with measurements and the guidelines provide advice on the differing standards of validation which may be applied including the manufacture and testing of validation mock-ups.

This paper is part of a Themed Issue on Measurement, modelling and mitigation of residual stress.     

Finite element analysis of chip formation and residual stresses induced by sequential cutting in side milling with microns to submicron uncut chip thickness and finite cutting edge radius

In this paper,the effect of four sequential cuts in side milling of Ti6Al4 V on chip formation and residual stresses(RS) are investigated using finite element method(FEM).While the open literature is limited mainly to the studies of orthogonal sequential cutting with the constant uncut chip thickness greater than 0.01 mm,it is suggested herein to investigate not only the variable uncut chip thickness which characterises the down milling process,but also the uncut chip thickness in the sub-micron range using a finite cutting edge radius.For the resulting ductile machining regime,the characteristics of the chip morphology,the force profiles,the plastic deformation and temperature distributions have been analyzed.Furthermore,this study revealed that the RS should be extracted toward the area where the insert exits the workpiece in the FE simulation of the down-milling process.The simulation of a number of sequential cuts due to the consecutive engagements of the insert is required in order to capture the gradual accumulation of the RS before reaching an asymptotic convergence of the RS profile.The predicted RS are in reasonable agreement with the experimental results.     

Using three-dimensional finite element analysis for simulation of residual stresses in railway wheels

One of the most important issues in railway wheels is residual stresses. It is desirable to produce less residual stresses when possible and to decrease the remaining residual stresses in the wheels. The objective of this paper is to provide an estimation of the residual stresses in the rail wheel caused by the stress field from heat treatment process of a railway wheel. A three-dimensional nonlinear stress analysis model has been applied to estimate stress fields of the railway mono-block wheel in heat treatment process. After forging or casting, railway wheels are heat-treated to induce the desirable circumferential compressive residual stress in the upper rim. Finite element analysis model is presented applying the elastic–plastic finite element analysis for the rail wheel under variable thermal loads. Calculative analysis applying a finite element method (FEM) has been used to predict residual stresses. The quenching and annealing segments of the wheel manufacturing process are simulated using a decoupled heat transfer and stress analysis. Three-dimensional finite element analysis results obtained show good agreement with those achieved in field measurements.     

Analytical formulation of subsurface stresses during orthogonal cutting of FRPs

Subsurface stresses generated during orthogonal cutting of Uni-directional Fiber Reinforced Plastics (UD-FRPs) have been studied using a generalized plane strain anisotropic elasticity formulation. An inclined line-load profile has been chosen to be representative of the resultant cutting forces acting on the workpiece material during orthogonal cutting. The validity of this assumed formulation has been established by comparison with photoelastic fringe patterns available in literature. Relative angle between the resultant force and the fiber orientation of the workpiece material has been found to be the most significant parameter determining the stresses in the subsurface region of the cutting zone.     

Finite element based model for predicting induced residual stresses and cutting forces in AISI 1020 steel alloy

The application of finite element models is a promising method for ensuring part quality during machining to accurately predict induced residual stresses and cutting forces. The present study applied Analysis System software to formulate a 3D model to predict induced residual stress and forces for AISI 1020 alloy. Taguchi method was applied in the design of the experiment with three levels and three factors selected: Cutting speed, feed rate and depth of cut. For validation, stresses are measured using an x-ray diffractometer from the surface to a depth of 0.6 mm in steps of 0.2 mm. The cutting forces are determined using a force dynamometer. Simulation results showed that cutting speed, feed rate and depth of cut contributed 94.76 %, 0.048 %, and 0.11 % respectively. The predictive model equations were statistically significant with a p-value of <0.005. The average induced residual stress on the superficial layer from the experiment and simulation were −367.7 MPa and −365.6 MPa respectively. The average residual stresses obtained at depths of 0.2 mm, 0.4 mm, and 0.6 mm were −260 MPa, −233 MPa, and −211 MPa, respectively. The proposed model offers a potential solution to reducing the costs of experimental methods.     

Experimental and finite element simulation methods for rate-dependent metal forming processes

An experimental procedure and a finite element simulation method for rate-dependent metal forming processes are developed. The development includes the formulation of a tangential stiffness matrix for an axisymmetric solid finite element with four node, eight degree of freedom, quadrilateral cross-section. The formulation includes the effects of elasticity, viscoplasticity, temperature, strain rate and large strains. The solution procedure is based on a Newton-Raphson incremental-iterative method which solves the non-linear equilibrium equations and gives temperatures and incremental stresses and strains. Three examples are studied. In example 1, finite element simulation for the upsetting of a cylindrical workpiece between two perfectly rough dies is performed and the results are compared with alternative finite element solutions. In examples 2 and 3, both experimental and finite element studies are performed for the upsetting of a cylindrical billet and the forging of a ball, respectively. Annealed aluminium 1100 workpieces are used in both examples. For the finite element analysis, uniaxial compression tests are first performed to provide the material properties. The tests generate elastic moduli and two sets of stress-strain curves (quasi-static and constant strain rate), which are used to establish a rate-dependent material model for input. For both examples 2 and 3, comparisons between the experimental and finite element simulation results for the forming force vs. die displacement relations and also for the deformed configurations show good agreement. The versatility of finite element methods allows for displaying detailed knowledge of the metal forming process, such as the distributions of temperature rise, yield stress, effective stress, plastic strain, plastic strain rate, forming forces and deformed configurations, etc. at any instance during the forming process.     

Thermo-viscoplastic residual stresses in metal matrix composites

A three-dimensional thermo-viscoplastic ideal method is presented to determine the interfacial and cellular stresses which arise during and from manufacturing of an ideal periodic continuous unidirectional graphite/aluminum metal matrix composite (MMC) lamina. The particular manufacturing process examined is a liquid-infiltrated cast MMC with temperature excursions from the matrix melting temperature of 933 K to room temperature. The final stress state of the aluminum matrix is found to be in the vicinity of its room temperature yield strength and essentially independent of fiber volume fraction. The interface has compressive normal tractions with an insignificant shear traction component present for fiber volume fractions less than 0·70, while for higher volume fractions, approximately one-half the interface experiences tensile normal tractions. Increased fiber volume fraction lowers fiber axial stresses and decreases the uniformity of the interfacial tractions. The magnitude of the residual stress state can be reduced from the value obtained from a constant cooling rate history by using an alternative cooling profile which has a rapid initial cooling rate of 0·75 K/s until 400 K, and a subsequent slower cooling rate of 0·2 K/min.     

Shielding effects and residual stresses at cleavage due to pre-existing dislocations

The motion of pre-existing edge dislocations in an infinite linear elastic body is studied at initiation of crack growth and at quasi-static steady-state crack growth. Dislocation nucleation is assumed not to occur. Thus, the study concerns only dislocations that are present in the virgin material. A dislocation is assumed to glide if its driving force exceeds a critical value. Changes in dislocation density, crack tip shielding and residual stresses are obtained. The shielding of a stationary crack tip is found to be small compared with the shielding of a growing crack tip. At steady-state the residual stresses far behind the crack tip are tensile near the crack, decreasing to zero at a certain distance from the crack plane. It is shown that the shielding due to pre-existing dislocations, e.g., for cleavage in α-iron crystals may be considerable. This revised version was published online in July 2006 with corrections to the Cover Date.     

Improving finite element predictions of modes of vibration

A technique is presented whereby the standard finite element approximations used in vibration analysis are modified in order to allow them to accurately predict the frequencies of the higher modes. This is done by using the results of dispersion analysis of the numerical approximations. The method is applied to the longitudinal vibration of a bar, and is shown to give good results for a uniform bar, a bar with continuously varying properties, and a bar with a step change in properties. Dispersion correction gives improved accuracy for the flexural vibration of a beam. The results of the method are also applied to the mode superposition method of dynamic analysis, and again a marked improvement in performance is obtained.     

金属裂纹板复合材料胶接修补强度的弹塑性有限元预测

金属裂纹板经复合材料补片胶接修补后,其结构强度明显提高,但裂纹板中的裂纹会导致严重的应力集中现象,并易产生塑性变形,呈现强烈的材料物理非线性特性,需要采用弹塑性力学原理,进行复合材料胶接修复结构的静强度预测。为此,考虑金属板材料的非线性特性,建立了金属裂纹板复合材料胶接修补结构的弹塑性有限元模型,并通过试验验证了模型的有效性。在此基础上,提出了基于裂纹尖端的张开位移(COD)判据的拉伸强度预测方法,分析了修复结构的塑性应变、COD以及静拉伸强度。结果表明:相对于应力强度因子K判据, COD判据能更有效地预测修复试件的静拉伸强度。      

基于梯度降温的叠层制备热残余应力

针对叠层制备工艺的热残余问题,为消除传统的基于同步降温假设的理论解与实际热残余现象的差异,本文在充分考虑成形过程中沿长度和厚度方向形成的温度梯度的基础上,分别建立在层平面和厚度方向引起的热残余变形和应力的解析解,并根据不同叠层制备工艺,将降温梯度概括为同步降温、均等梯度降温、非均等梯度降温、瞬态降温的4种模式.算例表明,梯度降温会造成在层平面和厚度方向均产生热残余现象.讨论了4种梯度降温模式对热残余程度的影响,梯度越大影响越大;合理解释了同一种材料制备的工件也会因降温梯度而产生明显的弯曲变形;对于梯度材料,叠层制备顺序会显著影响热残余的程度.研究表明,梯度降温假设符合实际制备、工艺,更准确地揭示了叠层制备热残余现象产生的机理,优化制备工艺缩小降温梯度是解决热残余问题的有效途径.     

Finite element evaluation of residual stresses in thick plates

This paper makes use of the Finite Elements Method (FEM) to study and analyze residual stresses in the cold bending and welding of thick plates. The welding model consists of two steps: first, performing of the thermal transient analysis model; and second, the carrying out of the mechanical transient analysis based on the temperature pattern at each node on each particular time. Used in these models is the inelastic temperature-dependent material. The output of the model includes residual stresses and permanent distortion; these were then compared with verified experimental results. The validated model and the results exhibit satisfactory agreement up to a 15-percent difference. As for the cold bending of thick plates, it is modeled using another finite element model and the residual stresses and permanent curvature of the thick plates are computed numerically. Again, the FEM model was validated against some official experimental results and satisfactory agreement between them was observed. Finally, the effects of these two different sources of residual stresses were combined, the combined effects established, and the results then discussed.