Heat Generation during the Fatigue of a Cellular Al Alloy A. RABIEI, A.G. EVANS, and J.W. HUTCHINSON The heat generation from a notch during the compression-compression fatigue of a cellular Al alloy has been measured and compared with a model. The measurements indicate that heat is generated because of hysteresis occurring in narrow cyclic plastic zones outside the notch. This process continues until the notch closes. At closure, a brief period of heat generation arises because of friction along the notch faces. A plasticity model based on the Dugdale zone is shown to provide a reasonably accurate characterization of the heat generated, with the proviso that an “ineffective” zone be transposed onto the notch tip. It is found that the temperatures generated are too small to cause fatigue by thermal softening. A fatigue mechanism based on either geometric softening of the cells or crack growth in the cell walls is implied. I. INTRODUCTION exceeding 100 °C at frequencies in the 30 Hz range, again because of low its thermal conductivity. [5,6] To the authors’ CELLULAR metals have been shown to experience knowledge, there have been no studies either in metals or fatigue degradation in both tension and compression. [1,2] This polymers of heat generated locally around stationary cracks degradation is manifested as a rapid increase in strain after subject to cyclic loading. a quiescent nucleation period wherein strain accumulation occurs slowly and stably (Figure 1(a)). The consequence is an endurance limit occurring at some fraction of the mono- II. EXPERIMENTAL METHODS tonic flow strength. This limit may be used for design pur- The thermal measurements are performed on a well-char- poses. [2] As fatigue progresses, the effective Young’s acterized, commercially available, closed-cell Al alloy, hav- modulus decreases (Figure 1(b)), indicative of damage ing the trade name ALPORAS. [1,7–9] Rectangular compres- mechanisms operating in the material. [2] The abrupt increase sion specimens were cut from castings of this material by in strain beyond the nucleation stage occurs in discrete bands electrodischarge machining (EDM), as described else- which have a thickness equal to about one cell size. The where. [7] Most tests were performed on samples with dimen- mechanisms responsible for localizing the strains into bands sions of 65  55  55 mm. A few tests were conducted and limiting life have received minimal attention. Optical on narrower samples, 12-mm thick. A small elliptical hole observations have indicated that the cell walls encompassing (12  4 mm) was introduced into the center section by some of the relatively large cells are susceptible to plastic EDM. The minor axis of the hole was slightly larger than buckling at the peak stress [1] (Figure 2). These buckled walls the largest cells. [1] experience larger-than-average cyclic strains and submit to Accordingly, the hole provides a well-defined strain con- a cyclic softening mechanism that induces and spreads a centrator that should localize the onset of fatigue lateral degradation zone, which eventually collapses the degradation. material along an entire band. For testing, both ends of the specimen were thermally The exaggerated cyclic plastic strains implied by these insulated. This was achieved using inserts between the speci- observations suggest that heat is generated locally around men and the loading platens. This insulating layer was strain concentrators and that the thermal flux be a measure needed to prevent heat generated by friction at the platens, of the plastic work accompanying each strain cycle. The as well as by the cyclic operation of the testing machine, present article provides a demonstration of this local heating from diffusing into the test specimen. effect and connects the flux to the plastic deformation. It Testing was performed in a compression-compression also addresses the possibility that fatigue is governed by mode, using a servohydraulic machine subject to an R ratio thermal softening as a result of the heat generated. of 0.1 at a frequency  of 10 Hz. [1,2] The maximum stress Heat generation during crack growth and fatigue has pre- was varied between 0.8 and 0.95  0 , where  0 is the mono- viously been studied in the following two situations. [3–6] tonic plateau stress. [1,7,9] Strains were measured using a linear (1) In metals having low thermal conductivity, particularly variable displacement transducer and were recorded digi- amorphous Ti alloys, appreciable heat is generated during tally. Images obtained by optical microscopy and scanning rapid crack extension, with local elevations in temperature electron microscopy were taken during testing to character- around the crack reaching about 20 °C. [3,4] (2) In polymers ize the deformation phenomena. subject to generalized cyclic straining, appreciable heating Thermal imaging of one of the side surfaces was per- has been measured, with temperature elevations in PTFE formed using a high-resolution infrared (IR) camera (Amber–Galileo) with a 256  256 array and a 30 m pixel size. A 50 mm IR lens was used to provide a magnification A. RABIEI, Postdoctoral Fellow, and J.W. HUTCHINSON, Professor, are of 0.215 mm/pixel. The surface of the specimen was covered with the Division of Engineering and Applied Sciences, Harvard University, with a black thin film to control its emissivity. In order Cambridge, MA 02138. A.G. EVANS, Professor and Director, is with the to monitor small (0.1 °C) variations in temperature, an Materials Institute, Princeton University, Princeton, NJ 08540. Manuscript submitted May 7, 1999. integration time of 1.2 ms was selected, with 15 images METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 31A, APRIL 2000—1129