Incremental Computation Technique for Residual Stress Calculations Using the Integral Method

The Integral Method for determining residual stresses involves making surface deformation measurements within a sequence of small increments of material removal depth. Typically, the associated matrix equation for solving the residual stresses within each depth increment is ill-conditioned. The resulting error sensitivity of the residual stress evaluation makes it essential that data measurement errors are minimized and that the residual stress solution method be as stable as possible. These two issues are addressed in this paper. The proposed method involves using incremental deformation data instead of the total deformation data that are conventionally used. The technique is illustrated using an example ESPI hole-drilling measurement.     

Measurement of residual-stress distribution by the incremental hole-drilling method

The hole-drilling method is widely used to measure residual stresses in mechanical components. Recent developments have shown that strains measured on the surface during an incremental drilling can be related to residual-stress distribution. Researchers throughout the world have proposed different calibration methods which lead to more or less accurate results.The present paper discusses different approaches used. A new calibration method is proposed. We also show how finite-element analysis can be used to determine the correlation coefficients. The variation of the strains measured on the surface for each increment is due to, first, the residual stresses in the layer and, second, the change of the hole geometry. Most authors do not consider the latter aspect. Our results show that this causes a significant error in the experimental data. The finite-element method has been used to compute the coefficients for all types of strain-gage rosettes when the hole diameter is predetermined.Another problem of the hole-drilling method is the selection of the drilling tool. Two systems have been studied: ultra-high-speed air turbine and conventional milling machine. The method has been applied on both shot-peened and water-quenched test specimens. The results are successfully compared with the bending-deflection and the X-ray method.     

Measurement of residual stresses by the hole-drilling method: Influences of transverse sensitivity of the gages and relieved-strain coefficients

The general expression of the error due to the transverse sensitivity of the gages and the relieved-strain coefficients, in a determination of residual stresses by the hole-drilling method in thin plates, is given. It has been shown that the transverse sensitivity of the gages can be ignored. A moderate amount of error, however, is introduced in the measurement of residual stresses when the relieved-strain coefficients from methods other than double integration over the area of the grid are used. The error due to the use of improper relieved-strain coefficients from rigorous relationships for calculation of residual stresses has been compared with the same part of the error from nonrigorous relationships. Abandonment of the use of nonrigorous relationships is recommended.     

Two Dimensions Residual Stresses Analysis Through Incremental Groove Machining Combined with Electronic Speckle Pattern Interferometry

In this study a new residual stress determination method in two directions simultaneously is presented. This method is based on stresses relaxation in a groove that is machined incrementally. The residual stresses relaxation occurs simultaneously from both the depth and the length of the groove. Thus, measuring the surface strain field generated by the relaxation enables to determine the stress gradient both along the depth and the length of the groove. To measure the surface strain in a direction perpendicular to the groove, a digital speckle pattern interferometer is used. This method is suitable when the residual stress field in the structure varies in the depth as well as along the surface of the part, like for example in a welded structure. The method is tested here on an aluminium plate in which a central band has been shot peened.     

Slitting Measurement of Residual Hoop Stresses Through the Wall-Thickness of a Filament Wound Composite Ring

The slitting method was used to determine residual hoop stress profile along the thickness of a filament wound carbon/epoxy ring. The method involves measuring strains at the inner surface of the ring, while a narrow axial slit is cut progressively from the outer surface. In order to calculate the residual hoop stress profile over the entire ring thickness, pulse method was used, which assumes that stress in each depth increment is uniform. Besides, Tikhonov regularization was employed to stabilize the stress results and reduce its sensitivity to strain measurement errors. Regarding the fact that Tikhonov regularization is not appropriate for computing solutions with discontinuities, pulse method coupled with Tikhonov regularization was used separately for each layer of the composite ring.     

A finite-element technique to analyze the data measured by the hole-drilling method

A finite-element technique to analyze the data obtained by the hole-drilling strain-gage method is presented. In this study, residual stresses are assumed as initial stresses existing in the structural material or component. It is also assumed that the elimination of the initial stresses in the region of the drilled hole changes the measured strains. After putting initial stresses into displacement finite-element equations and comparing the stiffness matrix and the initial stresses matrix with those of the previous increment, equations relating unknown initial stresses and measured strains were obtained. By solving these equations, residual stresses were obtained. In this paper three examples are studied. In the first two examples, calibration constants C1 to be used in determining residual stress were calculated which varied with depth. In the third example, the data obtained by using the hole-drilling method are analyzed. All examples show good agreement with previous studies. Using the present method allows greater flexibility of choice of specimen shape, materials, and experimental procedure than would be possible if only analytic solutions were used.     

Extending the stress-analysis range of brittle coatings

In this paper, an attempt is made to extend in both directions the range of the stresses that can be determined using brittle coatings: (1) by sensitizing the coating to determine small stresses, and (2) by the use of a new calibration device that allows the application of very large strains. The increase in sensitivity is obtained by bathing the coating with cold water under load. The coating used in this manner is shown to have a strain sensitivity as low as 100 μin./in., well below the 400 μin./in. limit imposed by crazing of the coating as it is normally used. The fixture to apply large strains is described and the method applied to several brittle coatings to calibrate them up to 10,000 μin./in. (1 percent) strain sensitivity. In conjunction with the above studies, a short test was conducted on the effects of repetitive loading on a brittle coating. Load history was shown to affect strain sensitivity in some cases.     

Method of calculating residual stresses in semicircular notches in a surface hardened hollow cylindrical specimen

A method is proposed to study the distribution of residual stresses in a semicircular notch in a hollow cylindrical specimen after advanced surface plastic deformation. The initial information used in the method is one or two experimentally determined components of the residual stress tensor in the hardened layer of the smooth specimen. The problem is solved using a finite element technique taking into account initial plastic strains, which are set in correspondence to the residual stresses according to the laws of elasticity. The effect of the hardening technology and notch depth on the distribution of residual stresses is studied. Experimental verification of the method showed that the calculated and experimental data on the stress distribution over the depth of the layer are in good agreement.     

Determining reliable edge isopachic data from interior thermoelastic measurements

The maximum stresses in a plane-stressed component typically occur on the boundary. However, it is generally difficult to obtain reliable experimental data at an edge and thermoelastic stress analysis is no exception. The inability to measure reliable edge isopachic stresses has caused many previous thermoelastic stress analyses to be more qualitative than quantitative. This paper develops and implements an effective iterative least-squares method for calculating reliable edge isopachic stresses from measured interior values. The method is based upon the plane-stress isotropic compatibility equation. A regularization scheme is employed to minimize the sensitivity to measurement error and to improve the stability of the algorithm by controlling the rate of convergence. An illustrative example with actual measured thermoelastic data is included. The processes thermoelastically determined results compare well with those obtained using strain gages.Paper was presented at the 1994 SEM Spring Conference held in Baltimore, MD on June 6–8.     

A highly sensitive noncontacting electromagnetic device for detecting dynamic stress in structures

A highly sensitive, noncontacting electromagnetic device has been developed to detect stress waves in structures. It is shown that for detecting an induced strain this device is over 500 times more sensitive than conventional bonded strain gages. The principle of detecting the strain by this device is based on the fact that dynamic stresses in a structure induce similar stresses in a bonded piezoelectric material. This, in turn, creates a magnetic field which extends beyond the material itself. An electromagnetic device has been built to detect this magnetic field and thus monitor the dynamic stresses. This method provides a noncontacting means of measuring strain in structures with improved sensitivity.     

Comparison of residual-stress variation with depth-analysis techniques for the hole-drilling method

Numerous data-analysis techniques have been developed to determine residual-stress information from strain data obtained from the hole-drilling method. The most commonly used technique for data analysis was developed by Rendler and Vigness (which forms the basis of the standard described in ASTM E837-85). A numerical development which was a model of the hole-drilling procedure has been used to determine stress variation with depth. A rigorous finite-element method to specifically analyze stresses in discrete hole increments has been developed. To evaluate these data-analysis techniques, three different computer-simulated stress fields are compared. The stress fields include a uniaxial stress that is constant with depth, a bending stress that varies linearly with depth, and a subsurface stress reversal. (The basis for this comparison is a finite-element developed technique. Its accuracy will be discussed later.) All data-analysis techniques showed excellent agreement for the uniaxial stress constant with depth test case. However, for the other two stress fields, significant discrepancies were apparent. Results are compared and discussed.     

残余应力测定的围箍压痕法模拟

本文从同工量测方法得到启发，提出了一种新型的残余应力测试方法－围箍压痕法。采用轴对称弹塑性有限元计算模拟了围箍压痕法测量结构残余应力的力学过程，得到了围箍压痕时不同残余应力程度下材料的变形，塑性区和接触应力分布。     

基于应变率阶跃测试的晶体铜压入应变率敏感性研究

纳米压入测试可以原位获取材料的诸多力学性能,包括弹性模量,硬度,屈服应力,应变率敏感指数等。本文利用应变率阶跃测试技术对多晶铜试样的应变率敏感性进行测试分析,硬度-位移曲线表明压头下方所存在的变形梯度对各阶跃应变率下的硬度值存在明显影响;采用基于晶体细观机制的塑性应变梯度理论对压入变形梯度效应予以修正,比较了修正与未修正数据所得的应变率敏感指数,在有效剔除压入变形梯度影响的基础上,应变率阶跃测试可实现单次压入下材料应变率敏感性的测试表征。     

异质双材料粘接梁的界面端部应力及端部龟裂破坏的实验应力分析

本文采用了高灵敏度的云纹干涉法对异质双材料粘接梁在弯曲载荷作用下的位移进行了测量，用局部杂交法对界面端部区域的应变和应力进行了计算。通过对该区域内的实验应力分析发现：拉应力σｘ是影响结构强度的关键因素。本文还对在基体材料表面近角点区域可能出现的龟裂破坏的原因进行了分析。     

沥青混合料车辙变形的离散元数值模拟

采用Burgers模型描述沥青基质的粘弹性,根据实验数据确定Burgers模型参数。借助数字图像处理方法建立试件几何模型,利用离散元法开展了车辙变形的离散元数值模拟,研究了沥青混合料在不同骨料分布、不同载荷和不同温度条件下的车辙深度变化情况。结果表明：温度对车辙变形的影响在沥青软化点附近较大,在离开软化点的范围较小;当温度较低时,混合料的整体性比较好,骨料分布对局部车辙变形的影响比较小,超载引起的车辙增量不太明显,而当温度达到或超过沥青软化点时,混合料的整体性明显下降,骨料分布对局部车辙变形的影响非常突出,超载引起的车辙增量也非常显著。因此,当超载和高温组合到一起时,车辙变形会大幅度增加,将给路面安全带来严重隐患。     

Analysis of residual stresses in bars and tubes of cylindrically orthotropic materials

One of the most frequently used techniques of determining residual stresses in cylindrical bodies of elastically isotropic materials is the Mesnager-Sachs boring-out method. This method is adequate for many engineering materials; however, certain materials possess elastic properties which vary with direction. Materials having one fairly common kind of directional variation are known as cylindrically orthotropic materials. Heretofore, no means has been available for determining the residual stresses from strain data taken after successive borings of members made of such materials. This paper gives the derivation of equations for this purpose along with graphs depicting the error to be expected if the data had been reduced by the Sachs equations.     

Stress distribution about a slowly growing crack determined by photoelastic-coating method

An experimental stress-analysis technique using a birefringent coating is reported for determining the stress distribution about a slowly growing crack. The maximum error of the test method for a large strain gradient is found to be less than 10 percent. For a plate with an internal crack, the experimentally determined stress distribution compares favorably with two numerical solutions. Comparison of stresses about an internal or double-edge crack to those about a single-edge crack indicates that the isochromatics bend over to about 45 deg with the plane of the crack in the former and are inclined at about 60 deg in the latter. Also, the stresses for a single-crack tip vary as the inverse square root of the radius, while the stresses for a double-crack tip follow anr ^?1/4 law more closely.     

各向同性率无关材料本构关系的不变性表示

在内变量理论的框架下,针对各向同性率无关材料,使用张量函数表示理论建立了塑性应变全量及增量本构关系的最一般的张量不变性表示. 它们均由3个完备不可约的基张量组合构成,这3个基张量分别是应力的零次幂、一次幂和二次幂. 因此得出,塑性应变、塑性应变增量与应力三者共主轴. 通过对基张量的正交化,给出了本构关系式在主应力空间中的几何解释. 进一步,全量(或增量)本构关系中3个组合因子被表达为应力、塑性应变(或塑性应变增量)的不变量的函数. 当塑性应变(或塑性应变增量)的3个不变量之间满足一定关系时,所给出的本构关系将退化为经典的形变理论(或塑性势理论).最后,还讨论它与奇异屈服面理论的关系,当满足一定条件时,两者是一致的.      

Effects of a roller and a tracked vehicle on the compaction of a high lifted decomposed granite sandy soil

The aim of this research was to innovate a new compaction machinery by comparing experimentally the effects of a two-axle, two wheel road roller and a tracked vehicle on the compaction of a decomposed granite sandy soil with a high spreading lift. By measuring the amount of sinkage of the terrain surface, the dry density distribution versus depth using a cone penetrometer, the normal earth pressure distribution versus depth using a stress state transducer (SST), the effects of the road roller and the tracked vehicle on the increment of the soil dry density were considered theoretically. It was observed that the tracked vehicle showed a larger amount of sinkage and a larger dry density distribution versus depth than the roller. The ratio of shear stress to normal stress was still large enough at the deep stratum, so that an optimal shear strain was developed on the whole range of the high lifted stratum and it increased the soil compaction density due to the dilatancy effect.     

Enhanced measurement of strain distributions

A theoretical approach is presented that uses multiple strain gages to accurately measure complicated strain distributions. The technique is based on the method of weighted residuals in conjunction with measured strain data and is applicable for arbitrary in-plane strain distributions. Conventional measurements using strain gages are shown to represent a particular case of the approach presented. The experimental characterization of unidimensional strain fields is discussed in detail. Two approaches are presented; these are based on linear and quadratic approximations of the strain field. The strain distribution for two important practical problems is evaluated assuming ideal conditions to assess the performance of the proposed approach. In both cases, the simulated results demonstrate that measurement error resulting from the finite size of a strain gage may be reduced. That is, a larger strain gage may be used for a given maximum admissible error. The method also allows a minimal error of measured nonlinear strains.