This is a proposal to fund a domestic PhD candidate to definitively assess the existence of long-range internal stresses (LRIS) in plastically deformed materials. Backstresses or LRIS in the past have been suggested by many (but certainly not all) to exist in plastically deformed crystalline materials. Elevated stresses can be present in regions of elevated dislocation density or dislocation heterogeneities in the deformed microstructures. The heterogeneities include edge dislocation dipole bundles (veins) and the edge dipole walls of persistent slip bands (PSBs) in cyclically deformed materials and cell and subgrain walls in monotonically deformed materials. The existence of long-range internal stress is especially important for the understanding of cyclic deformation and also monotonic de-formation. Preliminary x-ray microbeam diffraction experiments that are able to deter-mine the elastic strains within the cell interiors were performed by the principal investi-gator using a synchrotron. These were accomplished using, oriented, monotonically and cyclically (presaturation, i.e., no PSBs) deformed Cu single crystals. The results suggest that small (17 to 29 % of the applied stress) long-range internal stresses may be present in cell interiors. These LRIS vary substantially from cell to cell as 0-50% the applied stress. This proposal includes an attempt to measure elastic strains in the cell walls which has been challenging due to the high defect density. This will help complete the definitive analysis of LRIS in deformed materials. Finally, detailed transmission electron micros-copy will be performed on the dislocation substructure (Burger?s vector analysis and pre-cise spatial positioning of wall dislocations), to assess through a dislocation dynamics code, a verification of the experimental LRIS. The understanding of plastic deformation, in general, is expected to be enhanced. We expect to be the first to definitively assess long-range internal stresses in plastically deformed materials.


This is a project to uncover the secrets of the strength of materials using x-ray mi-crobeams. The use of intense, submicron, x-ray beams at the Advanced Photon Source in Illinois has led to the discovery that structural materials are under significant, variable internal stresses of opposite direction on submicron length scales corresponding to the dislocation substructure. This result has profound implications for understanding the me-chanical strength and behavior of materials. The presence of counterbalanced stresses within microscopic volumes (or cells) in deformed materials was predicted more than two decades ago and has been inferred from numerous indirect experiments. Yet, direct proof of their existence has been elusive, as spatially-resolved measurements of the stress mag-nitudes and distributions critical for testing theories and computer modeling were not possible before the development of high-resolution x-ray microbeams at synchrotron sources. The implications of this work are of direct relevance to important practical prob-lems such as sheet metal forming (for example, in automobile production) and metal fa-tigue, the latter being responsible for most structural materials failures.

Project Report

The purpose of this project was to characterize the full internal stress-state of stressed materials. When crystalline materials (e.g. metals and ceramics) are plastically deformed, line atomic defects or dislocations are generated. The defects tend to be inhomogeneously distributed within the material. There has been investigations in the past that have suggested that this "coagulation" of dislocations can lead to regions in a material that have very high stresses that are much larger than the applied stress. Although the average stress in the material equals the applied stress, it has been suggested by prominent investigations that the local stress in the material has significant undulations. The difference between the local stress and the applied stress has been termed the "long range internal stress" (LRIS) The consequence of these large undulations are substantial: a.) Fundamentally, large local stresses may enable rate-controlling processes not achievable under the magnitude of the applied stress and lead to unexpected deformation mechanisms. b) Practically, the Bauschinger effect, which is the remarkable stress decrement in plasticity on reversal of the applied stress, may now be explained by high local-stress. The Bauschinger effect is the basic element of cyclic deformation or material fatigue, perhaps the principal cause of structural material failures. Understanding the Bauschinger effect also has enormous consequences for sheet-metal forming in the U.S. manufacturing sector that can lead to substantial cost-savings. This investigation developed and utilized the most advanced tools to characterize and understand LRIS in solids. We used a synchrotron at the Advanced Photon Source at Argonne National Laboratory. More specifically, we developed techniques to use sub-micron microbeams of high energy x-rays to probe small volumes buried deep in a stressed material, absent of confusing surface effects. We produced definitive results in single crystals of deformed copper crystals that are, currently, the finest results in the world. We discovered that long range internal stresses are present in both high and low dislocation density regions, but are much less than others have suggested for monotonically deformed metals. These finding need to be extended to more complex materials and deformation histories to extend and generalize our findings. However, our results suggest that so far, dramatic changes in stress are not present and new rate-controlling processes are not enabled beyond those that are expected at the applied stress. Furthermore, we now have evidence that the important Bauschinger effect, again, the basic element of metal fatigue and an important effect in material manufacturing, is probably explainable in terms of mechanisms independent of long-range internal stresses. This has important industrial consequences. Finally, the funds for this work produced one domestic PhD student and supported a second student from an under-represented group that is very close to graduating.

National Science Foundation (NSF)
Division of Materials Research (DMR)
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Diana Farkas
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University of Southern California
Los Angeles
United States
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