The Role of Servocontrolled Testing in the Development of the Theory of Viscoplasticity Based on Total Strain and Overstress

Abstract

The rate-dependent properties of AISI Type 304 stainless steel and of the high-strength Ti-7Al-2Cb-1Ta alloy obtained with tension specimens using a servocontrolled testing machine at room temperature are discussed. Tests involve strain rates between 10−8 and 10−2 s−1, strain rate changes, relaxation periods, stress rates between 10−1 and 102 MPa s−1, and creep periods. The viscoplasticity model based on total strain and overstress is introduced and shown to qualitatively reproduce the properties observed under strain control. The theory is then examined for its qualitative prediction under stress control, and it is found that the average creep rate need not increase with an increase in stress owing to the overstress (effective stress) dependence of the creep rate. Numerical experiments illustrate this property, which is then confirmed by real experiments. The theory has two material functions representing work hardening and rate dependence. A method of determining the function representing rate dependence from strain rate change tests is discussed. For Type 304 stainless steel this function is represented by two equivalent expressions which can be used from static (10−8 s−1) to dynamic strain rates (103 s−1). A rate sensitivity factor M (akin to the m-factor used in materials science) is introduced. It is shown to vary with overstress or strain rate.

Viscoplasticity based on overstress with a differential growth law for the equilibrium stress

“…Inviewof ( This choice makes g rare dependent, see (8). In this case k and g would both be responsible for race dependence and inverse rate-sensitlvity could be modeled (the stress decreases upon an increase in stress (strain) rate).…”

“…This approachhas beenverifiedfor monotonicloadingof Type 304 SS [8]and of a Ti alloy [9]. The purposeof the present paperis to presenta furtherdevelopment of the theoryof viscoplasticity basedon overstress for cyclicloading.…”

Phenomenological modelling of viscoplasticity

“…This fact enables the modeling of the highly nonlinear strain rate sensitivity of metals and alloys; the strain rate must be changed by orders of magnitude to obtain an appreciable effect on the stress level. Various k[ ]functions are discussed by Krempl [18].…”

“…Subsequently the overstress dependence was shown to be useful in explaining relaxation and creep behavior; see Kujawski et al [5] and Liu and Krempl [19]. Krempl and Kallianpur [8], and Krempl [18] have shown that anomalous creep behavior can be explained by the overstress dependence. It is also vital in modeling the relaxation behavior around a hysteresis loop where it is found that the relaxation or creep is much less pronounced in regions of nearly elastic slope than in regions of reduced slope.…”

Deformation behavior of solder alloys under variable strain rate shearing & creep conditions

“…Variable strain rate and load drop tests on one single test sample have been a very useful mechanical test technique to develop general state variable material constitutive equations [5]. This kind of tests usually requires advanced programming capability and accurate measurement for the mechanical testing system to catch the response of materials to sudden change in stress or strain.…”