In a tensile test of a bar or fiber formed from a transversely isotropic viscoelastic material, the initial motion in regions away from the clamps is a homogeneous uniaxial extension. If the applied tensile load is “tame ” in the sense that it is given by a piecewise smooth function of time, then during the early stages of loading, the homogeneous extension of the specimen is also tame. It is, however, often the case that at a time t,, previous to the instant of fracture, the motion departs from a tame homogeneous extension. The critical time t, is the “failure time ” of the specimen, i.e., the time at which the motion first changes character; t, precedes, often by a constant factor, the time at which neck-down is easily visible. The problem of calculating t, for a given loading program is here treated within the framework of the general theory of nonlinear simple materials with fading memory. For such materials the instantaneous tensile modulus, i.e., the derivative of the immediate change in tensile stress with respect to a sudden change in tensile strain, depends upon the previous history of the strain. Reasons are presented here for identifying t, with the earliest time to at which the instantaneous tensile modulus becomes zero. It is shown that at a time at which the instantaneous modulus vanishes one cannot arbitrarily assign the rate of change of tensile stress and have the motion remain in the class of tame homogeneous extensions
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