Thick helium-burning shell phase and the second blue loop

The evolutionary behavior of models undergoing the thick helium-burning shell phase is explored in detail as a function of mass and composition with a full quasi-static evolutionary code. Eighteen models are studied which span the ranges 3 M/sub sun/< or =M/sub asterisk/< or =11 M/sub sun/, 0.20< or =Y< or =0.36, and 0.001< or =Z< or =0.03. Reasons for the occurrence of the second blue loop are discussed. The appearance of the second blue loop is found to be sensitive to the initial mass and composition as well as to the size of the mixing length, the inclusion of semiconvection and convective overshoot, and the treatment of opacity and rotation. The lifetime of the second blue loop, when it occurs, is approximately 3--14% that of the first blue loop. Despite the sensitivity to the input parameters, only three basic patterns are distinguished for the second blue loop. Additional crossings of the Cepheid instability strip are possible during this phase, and such Cepheids could possibly be detected because of their rapid period changes