Michael B. Prime

Cross-Sectional Mapping of Residual Stresses by Measuring the Surface Contour After a Cut

A powerful new method for residual stress measurement is presented. A part is cut in two, and the contour, or profile, of the resulting new surface is measured to determine the displacements caused by release of the residual stresses. Analytically, for example using a finite element model, the opposite of the measured contour is applied to the surface as a displacement boundary condition. By Bueckners superposition principle, this calculation gives the original residual stresses normal to the plane of the cut. This contour method is more powerful than other relaxation methods because it can determine an arbitrary cross-sectional area map of residual stress, yet more simple because the stresses can be determined directly from the data without a tedious inversion technique. The new method is verified with a numerical simulation, then experimentally validated on a steel beam with a known residual stress profile.

Residual stress, stress relief, and inhomogeneity in aluminum plate

Abstract Through-thickness residual-stress profiles in rolled 7050-T74 aluminum plate were measured before and after stress relief by stretching (-T x 51). Measurement required adapting the crack-compliance method to measure both in-plane stress components. Unexpected features in the profiles could be explained by through-thickness yield strength variations caused by crystallographic texture.

Use of Inverse Solutions for Residual Stress Measurements

For most of the destructive methods used for measuring residual stresses, the relationship between the measured deformations and the residual stresses are in the form of an integral equation, typically a Volterra equation of the first kind. Such equations require an inverse method to evaluate the residual stress solution. This paper demonstrates the mathematical commonality of physically different measurement types, and proposes a generic residual stress solution approach. The unit pulse solution method that is presented is conceptually straightforward and has direct physical interpretations. It uses the same basis functions as the hole-drilling integral method, and also permits enforcement of equilibrium constraints. In addition, Tikhonov regularization is shown to be an effective way to reduce the influences of measurement noise. The method is successfully demonstrated using data from slitting (crack compliance) measurements, and excellent correspondence with independently determined residual stresses is achieved.

Laser Surface-contouring and Spline Data-smoothing for Residual Stress Measurement

We describe non-contact scanning with a confocal laser probe to measure surface contours for application to residual stress measurement. (In the recently introduced contour method, a part is cut in two with a flat cut, and the part deforms by relaxation of the residual stresses. A cross-sectional map of residual stresses is then determined from measurement of the contours of the cut surfaces.) The contour method using laser scanning is validated by comparing measurements on a ferritic steel (BS 4360 grade 50D) weldment with neutron diffraction measurements on an identical specimen. Compared to lower resolution touch probe techniques, laser surface-contouring allows more accurate measurement of residual stresses and/or measurement of smaller parts or parts with lower stress levels. Furthermore, to take full advantage of improved spatial resolution of the laser measurements, a method to smooth the surface contour data using bivariate splines is developed. In contrast to previous methods, the spline method objectively selects the amount of smoothing and estimates the uncertainties in the calculated residual stress map.

Uncertainty, Model Error, and Order Selection for Series-Expanded, Residual-Stress Inverse Solutions

Measuring the spatial variation of residual stresses often requires the solution of an elastic inverse problem such as a Volterra equation. Using a maximum likelihood estimate (least squares fit), a series expansion for the spatial distribution of stress or underlying eigenstrain can be an effective solution. Measurement techniques that use a series expansion inverse include incremental slitting (crack compliance), incremental hole drilling, a modified Sachs method, and others. This paper presents a comprehensive uncertainty analysis and order selection methodology, with detailed development for the slitting method. For the uncertainties in the calculated stresses caused by errors in the measured data, an analytical formulation is presented which includes the usually ignored but important contribution of covariances between the fit parameters. Using Monte Carlo numerical simulations, it is additionally demonstrated that accurate uncertainty estimates require the estimation of model error, the ability of the chosen series expansion to fit the actual stress variation. An original method for estimating model error for a series expansion inverse solution is presented. Finally, it is demonstrated that an optimal order for the series expansion can usually be chosen by minimizing the estimated uncertainty in the calculated stresses.

Quenching and Cold-Work Residual Stresses in Aluminum Hand Forgings: Contour Method Measurement and FEM Prediction

The cold-compression stress relief process used to reduce the quench-induced stresses in high-strength aerospace aluminum alloy forgings does not fully relieve the stresses. This study measured and predicted the residual stress in 7050-T74 (solution heat treated, quenched, and artificially overaged) and 7050-T7452 (cold compressed prior to aging) hand forgings. The manu- facturing process was simulated by finite element analysis. First, a thermal analysis simulated the quench using appropriate thermal boundary conditions and temperature dependent material properties. Second, a structural analysis used the thermal history and a temperature and strain-rate dependent constitutive model to predict the stresses after quenching. Third, the structural analysis was continued to simulate the multiple cold compressions of the stress relief process. Experimentally, the residual stresses in the forgings were mapped using the contour method, which involved cutting the forgings using wire EDM and then measuring the contour of the cut surface using a CMM. Multiple cuts were used to map different stress components. The results show a spatially periodic variation of stresses that results from the periodic nature of the cold work stress relief process. The results compare favorably with the finite element prediction of the stresses.

Modeling and Measurement of Residual Stresses in a Bulk Metallic Glass Plate

The recent advent of multi-component alloys with exceptional glass forming ability has allowed the processing of large metallic specimens with amorphous structure. The possibility of formation of thermal tempering stresses during the processing of these bulk metallic glass (BMG) specimens was investigated using two models: (i) instant freezing model, and (ii) viscoelastic model. The first one assumed a sudden transition between liquid and elastic solid at the glass transition temperature. The second model considered the equilibrium viscosity of BMG. Both models yielded similar results although from vastly different approaches. It was shown that convective cooling of Zr41.2Ti13.8Cu12.5Ni10Be22.5 plates with high heat transfer coefficients could potentially generate significant compressive stresses on the surfaces balanced with mid-plane tension. The crack compliance (slitting) method was then employed to measure the stress profiles in a BMG plate that was cast in a copper mold. These profiles were roughly parabolic suggesting that thermal tempering was indeed the dominant residual stress generation mechanism. However, the magnitude of the measured stresses (with peak values of only about 1.5% of the yield strength) was significantly lower than the modeling predictions. Possible reasons for this discrepancy are described in relation to the actual casting process and material properties. The extremely low residual stresses measured in these BMG specimens, combined with their high strength and toughness, serve to further increase the advantages of BMGs over their crystalline metal counterparts.

The Contour Method Cutting Assumption: Error Minimization and Correction

The recently developed contour method can measure 2-D, cross-sectional residual-stress map. A part is cut in two using a precise and low-stress cutting technique such as electric discharge machining. The contours of the new surfaces created by the cut, which will not be flat if residual stresses are relaxed by the cutting, are then measured and used to calculate the original residual stresses. The precise nature of the assumption about the cut is presented theoretically and is evaluated experimentally. Simply assuming a flat cut is overly restrictive and misleading. The critical assumption is that the width of the cut, when measured in the original, undeformed configuration of the body is constant. Stresses at the cut tip during cutting cause the material to deform, which causes errors. The effect of such cutting errors on the measured stresses is presented. The important parameters are quantified. Experimental procedures for minimizing these errors are presented. An iterative finite element procedure to correct for the errors is also presented. The correction procedure is demonstrated on experimental data from a steel beam that was plastically bent to put in a known profile of residual stresses.

Comparison of residual strains measured by X-ray and neutron diffraction in a titanium (Ti–6Al–4V) matrix composite

Abstract This research compares matrix thermal residual strains measured in a continuous fiber reinforced SiC/Ti–6Al–4V titanium matrix composite (TMC) using X-ray and neutron diffraction with finite element predictions. The strain dependence on the strains for several reflections (105, 204, 300, 213 and 312) of the matrix were explored at the surface (X-ray) and in the bulk (neutron). To determine the longitudinal surface strains from the X-ray measurements for comparison with the neutron values, the e φψ versus sin 2 ψ plots were extrapolated to ψ =90°. Continuum micro-mechanics based multi-ply finite element models (FEM) simulating rectangular and hexagonal fiber distributions were explored for calculating average surface and bulk strains. For different reflections, the experimentally determined surface measured strains ranged from +1904±424 to +2974±321 μ e and the bulk measurements ranged from +2269±421 to +3022±1134 μ e . These values contrast with the single valued FEM prediction of+3200 μ e which was the same for both the surface and the bulk.

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.