Measured Strain Relaxation Research Articles

Reliable Residual Stress Analysis for Thin Metal Sheets by Incremental Hole Drilling

Abstract Sheet metal–forming processes induce characteristic residual stress-depth gradients into technical components. Regarding thin metal sheets with thicknesses of only a few millimeters, or those in the sub-mm range, surface finishing processes, e.g., machining processes like grinding, polishing, lapping, or mechanical post–surface treatments, might cause significant distortions. These may result from intentionally induced one-sided residual stress distributions or residual stress redistributions through one-sided materials removal. For process assessment and control, accurate residual stress analysis is indispensable. However, in sheet metal formation, the residual stress state is often accompanied by pronounced crystallographic textures, which usually cause failure of the standard laboratory procedures. As an example, X-ray residual stress analysis according to the standard sin2ψ-method is not feasible for markedly textured material states because of curved 2θ-sin2ψ distributions. On the contrary, we have already shown that the incremental hole drilling method that uses case-specific calibration data and considers specimen thickness and crystallographic texture provides reliable stress evaluation. Hereby, for thin metal sheets, the appropriate support condition is very important since improper support can lead to significant restraints, i.e., the specimen fixture hinders the strain relaxation on the specimen’s surface during the hole drilling process, and, for nonflat sheets, even assembling stresses can be superimposed. Consequently, stress calculation based on the measured strain relaxation data leads to erroneous residual stress results in application of the incremental hole drilling method. This work is derived from the necessity of measuring residual stress-depth gradients in thin molybdenum sheets. Thereby, an appropriate specimen support strategy for hole drilling application on thin metal sheets is proposed based on a systematic parametric study using 3-D finite element modeling that considers different sheet thicknesses. Based on the simulation results, a support ring with an adequate inner diameter is proposed as the most suitable specimen support. The numerical findings were verified by experimental residual stress analyses with the use of two different specimen supports.

A load-holding time prediction method based on creep strain relaxation for the cold-stretching process of S30408 cryogenic pressure vessels

Austenitic stainless steel (ASS) has been widely used for cryogenic pressure vessels. Its high strain hardening characteristic allows cold-stretching. In the cold-stretching process, the load-holding time is a critical operating parameter which affects the final deformation of the material. In this paper, a load-holding time prediction method for the cold-stretching process of S30408 cryogenic pressure vessels is proposed, based on room-temperature creep strain relaxation. The proposed correlation has only one variable, the maximum circumferential stress applied to the cylindrical shell, which can be easily obtained by finite element analysis. Consequently, the strain rate measurement during the cold-stretching process is significantly simplified. The prediction method and the strain rate measurement were verified by experimental measurements conducted on two vessels manufactured via the cold-stretching process. The measured strain relaxation times accurately matched the calculated values and the load-holding time for the process was well predicted.

Application of the Incremental Hole-Drilling Method on Thick Film Systems—An Approximate Evaluation Approach

A new evaluation procedure is presented regarding the application of the incremental hole-drilling technique to determine in-depth residual stress distribution in thick film systems. Using a direct correction of the measured strain relaxation, obtained after each incremental depth, to take into account the effect of the layered structure of the material, the standard evaluation procedures can still be used without any further modification. For example, the standardized integral method uses specific geometrical calibration constants, which are only valid for isotropic, homogeneous and linear elastic materials. Using artificial neural networks, for the prediction of the correction function to be applied to the measured strain relaxation in thick layered systems, the standard integral method can still be applied. The validation of the proposed approach is shown using finite element (FE-) simulations. In addition, the new evaluation strategy is applied for residual stress determination in a thermally sprayed Aluminum oxide coating on a steel (S690QL) substrate.

Strain relaxation in AlGaN multilayer structures by inclined dislocations

To examine further the strain relaxation produced by inclined threading dislocations in AlGaN, a heterostructure with three AlGaN layers having successively increasing Ga contents and compressive strains was grown on an AlN template layer by metalorganic vapor-phase epitaxy. The strain state of the layers was determined by x-ray diffraction (XRD) and the dislocation microstructure was characterized with transmission electron microscopy (TEM). As the GaN mole fraction of the heterostructure increased from 0.15 to 0.48, the increased epitaxial strain produced inclined dislocations with successively greater bend angles. Using the observed bend angles, which ranged from 6.7° to 17.8°, the measured strain relaxation within each layer was modeled and found to be accounted for by threading-dislocation densities of 6–7×109/cm2, in reasonable agreement with densities determined by TEM and XRD. In addition to the influence of lattice-mismatch strain on the average bend angle, we found evidence that local strain inhomogeneities due to neighboring dislocations influence the specific bend angles of individual dislocations. This interaction with local strain fields may contribute to the large spread in the bend angles observed within each layer. A detailed TEM examination found that the initial bending of threading dislocations away from vertical often occurs at positions within <15 nm of the AlGaN/AlN heterointerface. Under the assumption that dislocation climb mediated by bulk-defect diffusion is effectively suppressed at the growth temperature, this result implies that inclination is established by processes occurring at the dynamic growth surface. We describe a mechanism where dislocation bending occurs by means of dislocation-line jogs created when surface steps overgrow vacancies that attach to threading-dislocation cores at their intersection with the growth surface.

A quantitative procedure to probe for compositional inhomogeneities in In xGa 1−xN alloys

The distribution of indium in a GaN/In x Ga 1− x N/Al y Ga 1− y N quantum well with x±Δ x=0.24±0.07 is quantitatively investigated by extraction of displacement fields from lattice images. Simulations accurately describe the measured strain relaxation across a wedge-shaped sample for a sample thickness up to 150 nm. The proportionality between indium concentration and resulting lattice constant c( x) is approximated by c( x)=0.5185+0.111 x nm. In general, it is challenging to discriminate the effects of random alloying against clustering. In In x Ga 1− x N this is particularly true at low indium concentrations x<0.2. For an accurate quantitative analysis, sample preparation and imaging were developed such that radiation damage can be recognized if present. Further, an analysis of detection limits and knowledge of the sample thickness are crucial for obtaining reproducible results. Data averaging is necessary to reach sufficient precision. Consequently, the size of the indium-rich clusters is poorly known if x is small. Beyond the interest in physical properties of In x Ga 1− x N alloys, the analysis of strain and its relaxation exemplifies how quantitative analysis is possible at an atomic level and is in excellent agreement with theoretical predictions.

Elastic strain relaxation in free-standing SiGe/Si structures

We have investigated elastic strain relaxation, i.e., strain relaxation without the introduction of dislocations or other defects, in free-standing SiGe/Si structures. We fabricated free-standing Si layers supported at a single point by an SiO2 pedestal and subsequently grew an epitaxial SiGe layer. The measured strain relaxation of the SiGe layer agrees well with that calculated using a force-balance model for strain sharing between the SiGe and strained Si layers. We report strained Si layers with biaxial tensile strain equal to 0.007 and 0.012.

In situ measurements of temperature-dependent strain relaxation of Ge/Si(111)

We have measured strain relaxation and clustering in Ge films grown by molecular beam epitaxy on Si(111) at substrate temperatures between 450 and 700 °C in real time with reflection high energy electron diffraction (RHEED). At 450 °C, we observe an oscillation of the surface lattice constant for the first 3.5 bilayers [(BLs) thicknesses were calibrated by Rutherford backscattering spectrometry], followed by a sharp two-dimensional–three-dimensional (2D–3D) growth mode transition, when transmission diffraction features appear in RHEED. The surface lattice constant then begins to relax at an initial rate of about 0.5%/BL. The mechanisms of island growth and strain relaxation change with growth temperature. At 500 °C, the surface lattice constant begins to relax after only 1 BL, and at 550 °C relaxation begins immediately. At both temperatures, however, 3D spots do not appear until after 3.5 BL. The initial rate of strain relaxation decreases with increasing temperature until, at 700 °C (when 3D spots never appear), it is only 0.04%/BL. This behavior may be explained by a temperature-dependent roughness length scale. At low temperature, atomic force microscope images show the development of small (∼1000 Å), faceted islands with aspect ratios (height/width) on the order of 0.07. With increasing temperature, the formation of well-defined facets is inhibited. At 700 °C, islands grow very large from the outset, with aspect ratios less than 0.015. The islands are unable to thicken much, because dislocations can glide in easily at the edges, enabling the islands to grow laterally quickly. The strain in the “new” islands is not substantially less than that in the “old” islands. At the highest temperatures used, diffusion becomes a relevant mechanism for strain relief.

In-Situ Measurements of Islanding and Strain Relaxation of Ge/Si(111)

AbstractWe have measured strain relaxation and islanding in Ge films grown by molecular beam epitaxy on Si(111) at substrate temperatures between 450°C and 700°C in real time with reflection high energy electron diffraction (RHEED). At 450°C, we observe an oscillation of the surface lattice parameter for the first three bilayers (BL), followed by a sharp 2D–3D growth mode transition, when transmission diffraction features appear in RHEED. The surface lattice parameter then begins to relax at an initial rate of about 0.5%/BL. The mechanisms of island growth and strain relaxation change with growth temperature. At 500°C the surface lattice parameter begins to relax after only 1BL; at 550°C relaxation begins immediately. However, 3D spots do not appear until after 3.5BL at either temperature. The initial rate of strain relaxation decreases with increasing temperature until, at 700°C (when 3D spots never appear), it is only 0.04%/BL. This behavior may be explained by a temperature-dependent roughness length scale, as well as by differences in dislocation nucleation at low and high temperatures. At low temperature, atomic force microscope images show the development of small (1000Å), faceted islands with aspect ratios (height/width) on the order of 0.07. The formation of well-defined facets is inhibited at higher temperatures. At 700°C, islands grow very large (lμm) from the outset, with aspect ratios less than 0.015. These islands cannot thicken much, because dislocations can glide in easily at their edges. The islands grow laterally quickly, and the strain in the “new” islands is not substantially less than that in the “old.” At 700°C, 28% of the Ge/Si misfit strain may be relieved by diffusion.

Strain Relaxation and In-Situ Observation of Voiding in Passivated Aluminum Alloy Lines.

ABSTRACTStrain relaxation in passivated Al-0.5% Cu lines was measured using X-ray diffraction coupled with in-situ observation of the formation and growth of stress induced voids. Samples of 1 μm thick Al-0.5% Cu lines passivated with Si3N4 were heated to 380ºC, then cooled and held at 150ºC. During the test, principal strains along the length, width, and height of the line were determined using a grazing incidence x-ray geometry. From these measurements the hydrostatic strain in the metal was calculated and strain relaxation was observed. The thermal cycle was duplicated in a high voltage scanning transmission electron microscope equipped with a backscattered electron detector. The 1.25 μm wide lines were seen to have initial stress voids. Upon heating these voids reduced in size until no longer observable. Once the samples were cooled to 150ºC, voids reappeared and grew. The measured strain relaxation is discussed in terms of void and θ-phase (Al2Cu) formation.

Strain Relaxation and In-Situ Observation of Voiding in Passivated Aluminum alloy Lines

AbstractStrain relaxation in passivated Al-0.5% Cu lines was measured using X-ray diffraction coupled with in-situ observation of the formation and growth of stress induced voids. Samples of 1 μm thick Al-0.5% Cu lines passivated with Si3N4 were heated to 380°C, then cooled and held at 150°C. During the test, principal strains along the length, width, and height of the line were determined using a grazing incidence x-ray geometry. From these measurements the hydrostatic strain in the metal was calculated and strain relaxation was observed. The thermal cycle was duplicated in a high voltage scanning transmission electron microscope equipped with a backscattered electron detector. The 1.25 μm wide lines were seen to have initial stress voids. Upon heating these voids reduced in size until no longer observable. Once the samples were cooled to 150°C, voids reappeared and grew. The measured strain relaxation is discussed in terms of void and θ-phase (Al2Cu) formation.

Near‐surface in situ stress: 2. A comparison with stress directions inferred from earthquakes, joints, and topography near Blue Mountain Lake, New York

At 11 outcrops within 100 km of Blue Mountain Lake, New York, we measured strain relaxation during overcoring of “surface,” “doorstopper,” and Bureau of Mines borehole deformation gauges. The majority of measurements showed a maximum expansion ε1 parallel with the contemporary tectonic stress field. To confirm further the orientation of in situ stress, at two sites, vertical fractures were induced at borehole walls using a packer‐fracturing technique. Several cores from each site were then tested for mechanical anisotropy using ultrasonic, compressibility, and thin section analyses. The orientations of mechanical anisotropy had a poor correlation with the preferred orientation of microcracks observed in thin section. The various techniques for measuring in situ stress orientations gave internally consistent results where ε1 generally aligned with topographic contours and often the mechanically stiff direction of the core. Furthermore, et aligned with the known contemporary tectonic stress, local p axes of earthquakes, Precambrian structures, and local joints. We interpret the alignment of ε1 and other structures to be the result of a feedback between the contemporary tectonic stress (ENE in the northeastern United States) and the process of jointing during the development of local topography. Hence ε1 is controlled by local structures and is a reflection of the contemporary tectonic stress but not a direct measure of it.