3D numerical simulation of drilling residual stresses

Drilling can affect the integrity of the surface of a mechanical component and reduce its fatigue life. Thus, drilling parameters such as lubrication or drilling velocity must be optimized to ensure a satisfactory residual mechanical state of the hole surfaces. Unfortunately, experimental tests are time consuming and it is not easy to observe the cutting process because of the confinement of the drill zone. The literature does not exhibit any numerical simulation capable of simulating 3D thermomechanical phenomena in the drill zone for large depth holes. Therefore, residual stresses cannot be easily simulated by means of the sole drilling parameters. The aim of this article is to propose a new numerical approach to compute drilling residual stresses for large-depth holes. A first simulation is developed to simulate heat transfer by means of a 3D thermoviscoplastic simulation in a new Rigid-ALE framework allowing the use of large calculation time steps. Then, a time interpolation and a spatial projection are implemented to rebuild the Lagrangian thermal history of the machined component. Finally, a thermo-elastoplastic simulation is carried out to compute residual stresses in the final workpiece. In this paper, the method is applied to a 316L austenitic stainless steel in the case of an unlubricated hole. The computed residual stresses are compared to experimental measurements.     

Optimal calculation steps for the evaluation of residual stress by the incremental hole-drilling method

The integral method is a suitable calculation procedure for the determination of nonuniform residual stresses by semidestructive mechanical methods such as the hole-drilling method and the ring-core method. However, the high sensitivity to strain measurement errors due to the ill conditioning of the equations has hindered its practical use. the analysis of the influence of the strain measurment error on the computed stresses carried out in the present work has showed that, given both maximum hole depth and number of total steps, the error sensitivity depends on the particular depth increment distribution used. By means of the matrix formulation, the depth increment distribution that optimizes the numerical conditioning is investigated. Numerical simulations and an experimental test have corroborated the best performance of the proposed step distribution with respect to the constant or increasing distributions commonly used.     

A semi-analytical elastic stress–displacement solution for notched circular openings in rocks

A semi-analytical plane elasticity solution of the circular hole with diametrically opposite notches in a homogeneous and isotropic geomaterial is presented. This solution is based on: (i) the evaluation of the conformal mapping function of a hole of prescribed shape by an appropriate numerical scheme and (ii) the closed-form solutions of the Kolosov–Muskhelishvili complex potentials. For the particular case of circular notches––which resemble to the circular cavity breakout in rocks––it is demonstrated that numerical results pertaining to boundary stresses and displacements predicted by the finite differences model FLAC^2D, as well as previous analytical results referring to the stress-concentration-factor, are in agreement with analytical results. It is also illustrated that the solution may be easily applied to non-rounded diametrically opposite notch geometries, such as “dog-eared” breakouts by properly selecting the respective conformal mapping function via the methodology presented herein. By employing a stress-mean-value brittle failure criterion that takes into account the stress-gradient effect in the vicinity of the curved surfaces in rock as well as the present semi-analytical solution, it is found that a notched hole, e.g. borehole or tunnel breakout, may exhibit stable propagation. The practical significance of the proposed solution lies in the fact that it can be used as a quick-solver for back-analysis of borehole breakout images obtained in situ via a televiewer for the estimation of the orientation and magnitude of in situ stresses and of strain–stress measurements in laboratory tests.     

Interaction of crack-tip and notch-tip stress singularities for circular cylinder in torsion

Singular integral equations are used to formulate the torsion problem of a circular cylinder containing a polygonal opening and a line crack. The formulation is based on degenerating a system of connecting line cracks to that of a polygon, the sides of which coincides with the cracks. Considered, in particular, is the torsion of a circular cylinder with a rectangular hole and a nearby slanted line crack. Mode III stress intensity factors are computed at both ends of the crack to reflect their relative position to the rectangular hole in addition to change in the dimensions of the crack relative to the other geometric variables. Recognizing that the singular behavior of the stresses near a reentrant's corner differs from that of the crack tip, intensification of the local stresses at the corners of the rectangular hole is also examined. The results show the influence of the crack size and position.     

A rational theory of oblique incidence and its extension to stress-separation in birefringent composites

A rational theory of oblique incidence for a birefringent medium is developed. The theory rules out the concept of secondary principal stresses as an arbitrary one and provides more adequate interpretation of isochromatics and isoclinics in oblique incidence. The method is shown to be applicable for stress-separation in an anisotropic-birefringent composite, and the stress-optical equations deduced require an additional stress-fringe constant to those involved in normal incidence. The stress-birefringence relations for isotropic photoelasticity are obtained as a particular case of the general theory.     

Computation of Bending Stress in Pipes Using Weighted Hole-Drilling and DSPI Measurements

Pipelines usually operate under bending and axial stresses, caused by external loads, combined with residual stress distributions (manufacturing stresses), which affect the mechanical behavior of the pipe. Despite its semi-destructive nature, the hole drilling technique and digital speckle pattern interferometry (DSPI) can be applied to determine combined stresses along a cross-section. To achieve this, a set of equally-spaced angular points spread along the cross-section perimeter are measured. For non-uniform stress computations the hole drilling technique frequently gives a detailed stress distribution which is related to the external layer (1 mm) of the pipeline. In order to obtain a representative and unique value for the stress acting at each point, a novel approach can be used to evaluate a weighted average stress from each available stress distribution and to identify possible outlier measured points. In accordance with this approach, weighting coefficients are calculated using some particular features found in the residual stress profiles of pipelines. A reference bending test bench was used to evaluate the proposed methodology and it verified good agreement between the reference and computed stresses.     

Solution of the moiré hole drilling method using a finite-element-method-based approach

The moiré hole drilling method in a biaxially loaded infinite plate in plane stress is an inverse problem that exhibits a dual nature: the first problem results from first drilling the circular hole and then applying the biaxial loads, while the other problem arises from doing the opposite, i.e., first applying the biaxial load and then drilling the circular hole. The first problem is hardly ever addressed in the literature but implies that either separation of stresses or material property identification may be achieved from interpreting the moiré signature around the hole. The second is the well-known problem of determination of residual stresses from interpreting the moiré fringe orders around the hole. This paper addresses these inverse problem solutions using the finite element method as the means to model the plate with a hole, rather than the typical approach using the Kirsch solution, and a least-squares optimization approach to resolve for the quantities of interest. To test the viability of the proposed method three numerical simulations and one experimental result in a finite width plate are used to illustrate the techniques. The results are found to be in excellent agreement. The simulations employ noisy data to test the robustness of this approach. The finite-element-method-based inverse problem approach employed in this paper has the potential for use in applications where the specimen shape and boundary conditions do not conform to symmetric or well-used shapes. Also, it is a first step in testing similar procedures in three-dimensional samples to assess the residual stresses in materials.     

Elastoplastic state of flexible conical shells with a circular hole under axial tension

The elastoplastic state of thin conical shells with a circular hole is analyzed assuming finite deflections. The distributions of stresses, strains, and displacements along the hole boundary and in the zone of their concentration are studied. The stress–strain state of shells around the hole under axial tension is analyzed taking into account two nonlinear factors. The numerical results are presented as plots and tables     

Influence of the viscoelastic properties of a composite on the stress distribution around an elliptic hole in a plate

The time variation in the stresses around an elliptic hole in a composite plate is studied. Solutions that characterize the effect of the time dependence of the relaxation moduli of the composite components on stresses are obtained. The solutions in the time domain are obtained from the elastic–viscoelastic analogy and the corresponding elastic solutions for the effective moduli of the composite and the stress field around an elliptic hole in an anisotropic plate. The inverse Laplace transformation is carried out by an effective numerical method     

Residual Stress Determination Using Hole Drilling and 3D Image Correlation

In recent years, the hole drilling method for determining residual stresses has been implemented with optical methods such as holographic interferometry and ESPI to overcome certain limitations of the strain rosette version of hole drilling. Although offering advantages, the interferometric methods require vibration isolation, a significant drawback to their use outside of the laboratory. In this study, a 3D image correlation approach was used to measure micron-sized surface displacements caused by the localized stress relief associated with hole drilling. Residual stresses were then found from the displacements using non-dimensional relations previously derived by finite element analysis. A major advantage of image correlation is that it does not require interferometric vibration isolation. Experiments were performed to check the ability of this new approach for uniaxial and equi-biaxial states of stress. Stresses determined by the approach were in good agreement with computed values and those determined by hole drilling using holographic interferometry.     

Mixed numerical–experimental technique for orthotropic parameter identification using biaxial tensile tests on cruciform specimens

This paper presents a mixed numerical–experimental method for the identification of the four in-plane orthotropic engineering constants of composite plate materials. A biaxial tensile test is performed on a cruciform test specimen. The heterogeneous displacement field is observed by a CCD camera and measured by a digital image correlation (DIC) technique. The measured displacement field and the subsequently computed strain field are compared with a finite element simulation of the same experiment. The four independent engineering constants are unknown parameters in the finite element model. Starting from an initial value, these parameters are updated till the computed strain field matches the experimental strain field. Two specimen geometries are used: one with a centered hole to increase the strain heterogeneity and one without a hole. It is found that the non-perforated specimen yields the most accurate results.     

A new analytical-numerical method for calculating interacting stresses of a multi-hole problem under both remote and arbitrary surface stresses

Based on the elementary solutions and new integral equations, a new analytical-numerical method is proposed to calculate the interacting stresses of multiple circular holes in an infinite elastic plate under both remote stresses and arbitrarily distributed stresses applied to the circular boundaries. The validity of this new analytical-numerical method is verified by the analytical solution of the bi-harmonic stress function method, the numerical solution of the finite element method, and the an...     

Stress-strain state of a flexible spherical shell with an eccentric circular hole

The stress-strain state of thin flexible spherical shells weakened by an eccentric circular hole is analyzed. The shells are made of an isotropic homogeneous material and subjected to internal pressure. A problem formulation is given, and a method of numerical solution with allowance for geometrical nonlinearity is outlined. The distribution of displacements, strains, and stresses along the hole boundary and in the region of their concentration is examined. The data obtained are compared with numerical solutions of the linear problem. The stress-strain state around the eccentric circular hole is analyzed with allowance for geometrical nonlinearity __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 10, pp. 92–98, October 2007.     

Use of characteristics method with cubic interpolation for unsteady-flow computation

The specified-time-interval (STI) scheme has been used commonly in applying the method of characteristics (MOC) to unsteady open-channel flow problems. However, with the use of STI scheme, the numerical error for the simulation results can always be induced due to the interpolation used to approximate the characteristics trajectory. Hence, in order to remedy the numerical errors caused by the interpolation, one needs to seek some kind of interpolation technique with higher-order accuracy. Instead of the linear interpolation technique, which has been used very commonly and can induce serious numerical diffusion, the Holly--Preissmann two-point, method, which is a cubic interpolation technique with fourth-order of accuracy, is proposed here to integrate with the method of characteristics for the computation of one-dimensional unsteady flow in open channel. The concept of reachback and reachout in space and time directions for the characteristics is also introduced to assure the model stability. The computed results from this new model are compared with those computed by using the Preissmann four-point scheme and the multimode method of characteristics with linear interpolation.     

Photoelastic determination of stresses in multiple-pin connectors

The design, fabrication, and testing of photoelastic models of double-lap, multiple-pin connectors are discussed. Interest is in the stresses in the inner laps. These stresses are determined by constructing models with photoelastic inner laps and transparent-acrylic outer laps. The connectors have two pins, in tandem, parallel to the load direction. A photoelastic-isotropic point is shown to permit the evaluation of load sharing between the two pins. A numerical scheme, utilizing the isochromatic- and isoclinic-photoelastic data and a finite-difference representation of the planestress equilibrium equations, is used to compute the stresses around the two pins. Representative stress distributions and stress-concentration factors are shown.     

一种激波稳定的对流-压力通量分裂格式

针对欧拉方程三种流行的对流-压力通量分裂方法(Liou-Steffen,Zha-Bilgen和Toro-Vázquez)进行特征分析,进而提出一种新的对流-压力通量分裂格式。采用Zha-Bilgen分裂方法将欧拉方程的通量分裂成对流项和压力项两部分,使用TV格式来计算这两部分的数值通量。利用压力比构造激波探测函数,并且在强激波附近的亚声速区域增加TV格式的剪切粘性来克服数值模拟中的激波不稳定性。数值算例的计算结果表明,新的对流-压力通量分裂格式不仅保留了原始TV格式精确分辨接触间断的优点,而且具有更好的鲁棒性,在数值模拟多维强激波问题时不会出现不稳定现象。因此,该格式是一种精确并且具有强鲁棒性的数值方法,可以广泛地应用于可压缩流体的数值计算中。     

Measurement and Prediction of Residual Stresses in Quenched Stainless Steel Components

Austenitic stainless steel cylinders and rings are spray water quenched to create residual stresses at or greater than the yield strength. The residual stresses are measured using neutron diffraction, and two mechanical strain relaxation methods: deep hole drilling and incremental centre hole drilling. This paper compares the measurements with predictions of quenching using finite element analysis. Also finite element analysis is used to mimic deep hole and incremental centre hole drilling methods and to reconstruct residual stresses as if they have been measured. The measurements reveal similar trends to the predictions but there is only limited agreement between their magnitudes. However, there is better agreement between the reconstructed stresses and the measurements. Both the two mechanical strain relaxation methods reveal that large discrepancies occur between measurements and predictions arise because of plasticity. Irrespective of this and surprisingly there is good agreement between deep hole drilling and neutron diffraction measurements.     

一维溃坝洪水波的高精度数值模拟

将ENO(Essentially Non-Oscillatory)格式和Runge-Kutta时间离散的思想应用于一维Saint-Venant方程组的求解,数值模拟溃坝洪水,得出了水位和流速的沿程分布。经与理论解比较可见,数值解在间断波附近没有出现数值振荡,水位和流速大小均符合较好,表明ENO格式是一类新的高精度无振荡差分格式,采用ENO格式所建立的高分辨率模型能够很好地模拟溃坝波的演进过程。     

Residual-stress determination through combined use of holographic interferometry and blind-hole drilling

Holographic interferometry is used to determine in-plane radial displacements due to release of residual stresses by hole drilling. A method is derived for relating radial displacements measured in three directions of illumination to the state of residual stress, analogous to relations used in the conventional strain-rosette technique. Residual stress is produced by an interference fit of two circular tubes. Agreement between stress determined holographically with a computed value and with that determined by the conventional technique is good. Advantages of the holographic technique in overcoming various shortcomings of the conventional technique are discussed. A modification of the holographic technique involving data collection in only two directions of illumination is described.