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A D V A N C E D M A T E R I A L S & P R O C E S S E S | S E P T E M B E R 2 0 2 0 3 0 (b) (a) thermally equilibrate, as with solution heat treat processes. As the material is cooled rapidly from this temperature, thermal conductivity, heat capacity, and coefficient of thermal expansion behav- ior of the material start to play a major role. The material’s outer layer will cool faster than its center. If the outer layer was not physically attached to the cen- ter material, it would contract, but it is physically connected and restrained from contracting by the internal materi- al, which is at higher temperature. This thermal battle results in initially placing the external material in tension and the internal material in compression. If the stresses are high enough to cause lo- cal yielding, then subsequent residual stresses will follow upon further cool- ing the entire volume to room tempera- ture. Formation of residual stress is due to the continued cooling, where surface material is plastically deformed in ten- sion and/or the interior material is de- formed in compression, because the internal material continues to cool and tries to contract. In this scenario, the external material restrains the inter- nal material from contracting and as it does, it places the external material in compression and the internal materi- al in tension. Once completely cooled to room temperature, the material will have an established internal bulk resid- ual stress that is in equilibrium (i.e., the volumetric summation of all tensile and compressive stresses must equal zero). For phase transformation-induced residual stresses, the method of gen- eration is slightly different, but also re- lies on local strain and strain history. As seen in the lower portion of Fig. 1, a ma- terial can be heated to a high tempera- ture and thermally equilibrated, such as a steel during an austenitizing process. Once this material is rapidly cooled and a phase change occurs within the sur- face material, which is accompanied by a local microstructural volume change, the outer material is placed in com- pression as it is being restrained from expanding by the internal material vol- ume. An example of this may be seen in austenite to martensite reactions and the associated volume expansion. If the stresses are sufficiently high to cause local yielding, one would expect resid- ual stresses to subsequently be formed. This is similar to the prior example, but further cooling results in the internal material transforming, expanding for the example of martensite formation. The internal material is now restrained from expanding by the already cooled external material. This places the in- ternal material in compression and the surfacematerial in tension once thema- terial is thermally equilibrated at room temperature. In this case, local yielding (surface versus center) leads to the re- sidual stresses. If the thermal cycling was performed such that the thermal gradients or extent of phase change stresses were controlled within a range where the local volumes were only elas- tically loaded during processing, then no residual stresses would result. This fact is the basis for many highly so- phisticated and controlled heat treat- ing processes, such as marquenching or the use of salt or polymer quenchants. External mechanically induced re- sidual stresses are also common, though some are intentional (i.e., peen- ing or low-plasticity burnishing) while others are not (i.e., abusive machining). For this mechanism of residual stress formation, local volumes of material are again strained beyond their yield strength, often in tension. The sur- rounding material that is not yielded restrains the deformed material, which results in the locally plastic strained material being put into compression and the adjacent non-yielded material to be placed in tension. This is the exact process by which surface compressive stresses are formed by shot peening, laser shot peening, and low plastici- ty burnishing. If the entire volume of material was loaded past the yield point and then the stress was released, the entire volume would have no residu- al stress. This is the principle behind mechanical stress relieving, common- ly used for aluminum material. Note that the entire volume must be strained past yield to result in complete stress relieving. This is difficult to do as me- tallic materials are not truly isotropic and grain level strains must be taken into account. Figure 2 illustrates how local yielding of a material will result in residual stress formation and how com- plete yielding of a volume can provide residual stress relieving. S – Starting Condition L – Loaded Condition U – Unloaded Condition Fig. 2 — Stress-strain curves for two regions (represented by circle and triangle points) within a volume of material. The two regions have different starting residual stresses. If the material is strained to a nominal low level (a), the region with tensile residual stress will result in local yielding, whereas the region with compressive residual stress will not. In contrast, if the material is strained to a larger amount that enables all regions to exceed the yield point (b), the material will result in no residual stress when unloaded, but each region will have experienced slightly different amounts of plastic strain. This concept can be applied to assess localized straining to induce intentional residual stress (hole expansion), for mechanical stress relieving or material/ components, or analysis of test specimens or components exposed to near yield stresses in static loading or fatigue.